{"id":4917,"date":"2016-05-19T09:49:00","date_gmt":"2016-05-19T04:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-3-6\/"},"modified":"2023-03-22T15:17:46","modified_gmt":"2023-03-22T09:47:46","slug":"ncert-solutions-for-class-10-maths-exercise-3-6","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-6\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Exercise 3.6"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-6\/#NCERT_Solutions_for_Class_10_Maths_Pair_of_Linear_Equations_in_Two_Variables\" >NCERT Solutions for Class 10 Maths\u00a0Pair of Linear Equations in Two Variables<\/a><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-6\/#1_Solve_the_following_pairs_of_equations_by_reducing_them_to_a_pair_of_linear_equations\" >1. Solve the following pairs of equations by reducing them to a pair of linear equations:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-6\/#2_Formulate_the_following_problems_as_a_part_of_equations_and_hence_find_their_solutions\" >2. Formulate the following problems as a part of equations, and hence find their solutions.<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-6\/#NCERT_Solutions_for_Class_10_Maths_Exercise_36\" >NCERT Solutions for Class 10 Maths Exercise 3.6<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-6\/#_Download_CBSE_Question_Paper_2018\" >\u00a0Download CBSE Question Paper 2018<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-6\/#CBSE_app_for_Class_10\" >CBSE app for Class 10<\/a><\/li><\/ul><\/nav><\/div>\n<div>\n<p>NCERT Solutions for Class 10 Maths Exercise 3.6 Class 10 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 10 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p style=\"text-align: center;\"><strong>NCERT solutions for Maths\u00a0Pair of Linear Equations in Two Variables\u00a0<a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-10-mathematics-pair-of-linear-equations-in-two-variables\/1205\/ncert-solutions\/5\/\">Download as PDF<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/10%20Maths%20Book.jpg\" alt=\"NCERT Solutions for Class 10 Maths Exercise 3.6\" width=\"171\" height=\"211\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Pair_of_Linear_Equations_in_Two_Variables\"><\/span>NCERT Solutions for Class 10 Maths\u00a0Pair of Linear Equations in Two Variables<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_Solve_the_following_pairs_of_equations_by_reducing_them_to_a_pair_of_linear_equations\"><\/span><strong>1. Solve the following pairs of equations by reducing them to a pair of linear equations:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<\/div>\n<div>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 44px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image001.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 44px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image002.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 47px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image003.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 47px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image004.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image005.png\" \/>+ 3<em>y <\/em>= 14<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image006.png\" \/> \u2212 4<em>y <\/em>= 23<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <img decoding=\"async\" style=\"height: 44px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image007.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 44px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image008.png\" \/><\/strong><\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.6<\/p>\n<p style=\"text-align: justify;\"><strong>(v) 7<em>x <\/em>\u2212 2<em>y <\/em>= 5<em>xy <\/em><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>8<em>x <\/em>+ 7<em>y <\/em>= 15<em>xy<\/em><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(vi) 6<em>x <\/em>+ 3<em>y <\/em>\u2212 6<em>xy <\/em>= 0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>2<em>x <\/em>+ 4<em>y <\/em>\u2212 5<em>xy <\/em>= 0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(vii) <img decoding=\"async\" style=\"height: 44px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image009.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 44px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image010.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(viii) <img decoding=\"async\" style=\"height: 44px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image011.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 44px; width: 174px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image012.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong><img decoding=\"async\" style=\"height: 44px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image001.png\" \/> \u2026 (1)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image002.png\" \/> \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">Let <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image013.png\" \/>= <em>p<\/em> and <img decoding=\"async\" style=\"height: 44px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image014.png\" \/>= <em>q<\/em><\/p>\n<p style=\"text-align: justify;\">Putting this in equation (1) and (2), we get<\/p>\n<p style=\"text-align: justify;\"><em><img decoding=\"async\" style=\"height: 42px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image015.png\" \/><\/em><\/p>\n<p style=\"text-align: justify;\">\u21d2 3<em>p <\/em>+ 2<em>q <\/em>= 12 and 6 (2<em>p <\/em>+ 3<em>q<\/em>) = 13 (6)<\/p>\n<p style=\"text-align: justify;\">\u21d2 3<em>p <\/em>+ 2<em>q <\/em>= 12 and 2p + 3q =13<\/p>\n<p style=\"text-align: justify;\">\u21d2 3<em>p <\/em>+ 2<em>q <\/em>\u2013 12 = 0 \u2026 (3) and 2<em>p <\/em>+ 3<em>q <\/em>\u2013 13 = 0 \u2026 (4)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 11\" style=\"height: 119px; width: 304px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image016.jpg\" alt=\"1\" \/><\/p>\n<p style=\"text-align: justify;\"><em><img decoding=\"async\" style=\"height: 44px; width: 315px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image017.png\" \/><\/em><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em><img decoding=\"async\" style=\"height: 42px; width: 188px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image018.png\" \/><\/em><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em><img decoding=\"async\" style=\"height: 42px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image019.png\" \/><\/em><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em><img decoding=\"async\" style=\"height: 42px; width: 123px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image020.png\" \/><\/em><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>p <\/em>= 2 and <em>q <\/em>= 3<\/p>\n<p style=\"text-align: justify;\">But <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image013.png\" \/>= <em>p<\/em> and <img decoding=\"async\" style=\"height: 44px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image014.png\" \/>= <em>q<\/em><\/p>\n<p style=\"text-align: justify;\">Putting value of p and q in this we get<\/p>\n<p style=\"text-align: justify;\"><em>x <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image021.png\" \/> and <em>y <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image022.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 47px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image003.png\" \/>\u2026 (1)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 47px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image004.png\" \/> \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">Let <img decoding=\"async\" style=\"height: 44px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image023.png\" \/>= <em>p<\/em> and <img decoding=\"async\" style=\"height: 47px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image024.png\" \/>= <em>q<\/em><\/p>\n<p style=\"text-align: justify;\">Putting this in (1) and (2), we get<\/p>\n<p style=\"text-align: justify;\">2<em>p <\/em>+ 3<em>q <\/em>= 2 \u2026 (3)<\/p>\n<p style=\"text-align: justify;\">4<em>p <\/em>\u2212 9<em>q <\/em>= \u22121 \u2026 (4)<\/p>\n<p style=\"text-align: justify;\">Multiplying (3) by 2 and subtracting it from (4), we get<\/p>\n<p style=\"text-align: justify;\">4<em>p <\/em>\u2212 9<em>q <\/em>+ 1 \u2013 2 (2<em>p <\/em>+ 3<em>q <\/em>\u2212 2) = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 4<em>p <\/em>\u2212 9<em>q <\/em>+ 1 \u2212 4<em>p <\/em>\u2212 6<em>q <\/em>+ 4 = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 \u221215<em>q <\/em>+ 5 = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>q <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 58px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image025.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting value of q in (3), we get<\/p>\n<p style=\"text-align: justify;\">2<em>p <\/em>+ 1 = 2 \u21d2 2<em>p <\/em>= 1\u21d2 <em>p <\/em>= \u00bd<\/p>\n<p style=\"text-align: justify;\">Putting values of p and q in (<img decoding=\"async\" style=\"height: 44px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image023.png\" \/>= <em>p<\/em> and <img decoding=\"async\" style=\"height: 47px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image024.png\" \/>= <em>q<\/em>), we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image026.png\" \/> and <img decoding=\"async\" style=\"height: 47px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 44px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= 4 and <em>y <\/em>= 9<\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.6<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image005.png\" \/>+ 3<em>y <\/em>= 14 \u2026 (1)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image006.png\" \/> \u2212 4<em>y <\/em>= 23 \u2026 (2) and Let <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image013.png\" \/>= <em>p \u2026 <\/em>(3)<\/p>\n<p style=\"text-align: justify;\">Putting (3) in (1) and (2), we get<\/p>\n<p style=\"text-align: justify;\">4<em>p <\/em>+ 3<em>y <\/em>= 14 \u2026 (4)<\/p>\n<p style=\"text-align: justify;\">3<em>p <\/em>\u2212 4<em>y <\/em>= 23 \u2026 (5)<\/p>\n<p style=\"text-align: justify;\">Multiplying (4) by 3 and (5) by 4, we get<\/p>\n<p style=\"text-align: justify;\">3 (4<em>p <\/em>+ 3<em>y <\/em>\u2013 14 = 0) and, 4 (3<em>p <\/em>\u2212 4<em>y <\/em>\u2013 23 = 0)<\/p>\n<p style=\"text-align: justify;\">\u21d2 12<em>p <\/em>+ 9<em>y <\/em>\u2013 42 = 0 \u2026 (6) 12<em>p <\/em>\u2212 16<em>y <\/em>\u2013 92 = 0 \u2026 (7)<\/p>\n<p style=\"text-align: justify;\">Subtracting (7) from (6), we get<\/p>\n<p style=\"text-align: justify;\">9<em>y <\/em>\u2212 (\u221216<em>y<\/em>) \u2013 42 \u2212 (\u221292) = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 25<em>y <\/em>+ 50 = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>y <\/em>= 50 \u2013 25 = \u22122<\/p>\n<p style=\"text-align: justify;\">Putting value of y in (4), we get<\/p>\n<p style=\"text-align: justify;\">4<em>p <\/em>+ 3 (\u22122) = 14<\/p>\n<p style=\"text-align: justify;\">\u21d2 4<em>p <\/em>\u2013 6 = 14<\/p>\n<p style=\"text-align: justify;\">\u21d2 4<em>p <\/em>= 20\u21d2 <em>p <\/em>= 5<\/p>\n<p style=\"text-align: justify;\">Putting value of p in (3), we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image013.png\" \/> = 5 \u21d2 <em>x <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, <em>x <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image029.png\" \/> and <em>y <\/em>= \u22122<\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> <img decoding=\"async\" style=\"height: 44px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image007.png\" \/> \u2026 (1)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image008.png\" \/> \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">Let <img decoding=\"async\" style=\"height: 44px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image030.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting this in (1) and (2), we get<\/p>\n<p style=\"text-align: justify;\">5<em>p <\/em>+ <em>q <\/em>= 2<\/p>\n<p style=\"text-align: justify;\">\u21d2 5<em>p <\/em>+ <em>q <\/em>\u2013 2 = 0 \u2026 (3)<\/p>\n<p style=\"text-align: justify;\">And, 6<em>p <\/em>\u2212 3<em>q <\/em>= 1<\/p>\n<p style=\"text-align: justify;\">\u21d2 6<em>p <\/em>\u2212 3<em>q <\/em>\u2013 1 = 0 \u2026 (4)<\/p>\n<p style=\"text-align: justify;\">Multiplying (3) by 3 and adding it to (4), we get<\/p>\n<p style=\"text-align: justify;\">3 (5<em>p <\/em>+ <em>q <\/em>\u2212 2) + 6<em>p <\/em>\u2212 3<em>q <\/em>\u2013 1 = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 15<em>p <\/em>+ 3<em>q <\/em>\u2013 6 + 6<em>p <\/em>\u2212 3<em>q <\/em>\u2013 1 = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 21<em>p <\/em>\u2013 7 = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>p <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image022.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting this in (3), we get<\/p>\n<p style=\"text-align: justify;\">5 (<img decoding=\"async\" style=\"height: 42px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image022.png\" \/>) + <em>q <\/em>\u2013 2 = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 5 + 3<em>q <\/em>= 6<\/p>\n<p style=\"text-align: justify;\">\u21d2 3q = 6 \u2013 5 = 1<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>q <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image022.png\" \/><\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.6<\/p>\n<p style=\"text-align: justify;\">Putting values of p and q in (<img decoding=\"async\" style=\"height: 44px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image030.png\" \/>), we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 148px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image031.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 3 = <em>x <\/em>\u2212 1 and 3 = <em>y <\/em>\u2013 2<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= 4 and <em>y <\/em>= 5<\/p>\n<p style=\"text-align: justify;\"><strong>(v)<\/strong> 7<em>x <\/em>\u2212 2<em>y <\/em>= 5<em>xy \u2026 <\/em>(1)<\/p>\n<p style=\"text-align: justify;\">8<em>x <\/em>+ 7<em>y <\/em>= 15<em>xy \u2026<\/em> (2)<\/p>\n<p style=\"text-align: justify;\">Dividing both the equations by xy, we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image032.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image033.png\" \/><\/p>\n<p style=\"text-align: justify;\">Let <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image013.png\" \/>= <em>p<\/em> and <img decoding=\"async\" style=\"height: 44px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image014.png\" \/>= <em>q<\/em><\/p>\n<p style=\"text-align: justify;\">Putting these in (3) and (4), we get<\/p>\n<p style=\"text-align: justify;\">7<em>q <\/em>\u2212 2<em>p <\/em>= 5 \u2026 (5)<\/p>\n<p style=\"text-align: justify;\">8<em>q <\/em>+ 7<em>p <\/em>= 15 \u2026 (6)<\/p>\n<p style=\"text-align: justify;\">From equation (5),<\/p>\n<p style=\"text-align: justify;\">2<em>p <\/em>= 7<em>q <\/em>\u2013 5<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>p <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image034.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting value of p in (6), we get<\/p>\n<p style=\"text-align: justify;\">8<em>q <\/em>+ 7 (<img decoding=\"async\" style=\"height: 42px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image034.png\" \/>) = 15<\/p>\n<p style=\"text-align: justify;\">\u21d2 16<em>q <\/em>+ 49<em>q <\/em>\u2013 35 = 30<\/p>\n<p style=\"text-align: justify;\">\u21d2 65<em>q <\/em>= 30 + 35 = 65<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>q <\/em>= 1<\/p>\n<p style=\"text-align: justify;\">Putting value of q in (5), we get<\/p>\n<p style=\"text-align: justify;\">7 (1) \u2212 2<em>p <\/em>= 5<\/p>\n<p style=\"text-align: justify;\">\u21d2 2<em>p <\/em>= 2\u21d2 <em>p <\/em>= 1<\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.6<\/p>\n<p style=\"text-align: justify;\">Putting value of p and q in (<img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image013.png\" \/>= <em>p<\/em> and <img decoding=\"async\" style=\"height: 44px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image014.png\" \/>= <em>q<\/em>), we get <em>x <\/em>= 1 and <em>y <\/em>= 1<\/p>\n<p style=\"text-align: justify;\"><strong>(vi)<\/strong> 6<em>x <\/em>+ 3<em>y <\/em>\u2212 6<em>xy <\/em>= 0 \u2026 (1)<\/p>\n<p style=\"text-align: justify;\">2<em>x <\/em>+ 4<em>y <\/em>\u2212 5<em>xy <\/em>= 0 \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">Dividing both the equations by xy, we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image035.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image036.png\" \/><\/p>\n<p style=\"text-align: justify;\">Let <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image013.png\" \/>= <em>p<\/em> and <img decoding=\"async\" style=\"height: 44px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image014.png\" \/>= <em>q<\/em><\/p>\n<p style=\"text-align: justify;\">Putting these in (3) and (4), we get<\/p>\n<p style=\"text-align: justify;\">6<em>q <\/em>+ 3<em>p <\/em>\u2013 6 = 0 \u2026 (5)<\/p>\n<p style=\"text-align: justify;\">2<em>q <\/em>+ 4<em>p <\/em>\u2013 5 = 0 \u2026 (6)<\/p>\n<p style=\"text-align: justify;\">From (5),<\/p>\n<p style=\"text-align: justify;\">3<em>p <\/em>= 6 \u2212 6<em>q<\/em><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>p <\/em>= 2 \u2212 2<em>q<\/em><\/p>\n<p style=\"text-align: justify;\">Putting this in (6), we get<\/p>\n<p style=\"text-align: justify;\">2<em>q <\/em>+ 4 (2 \u2212 2<em>q<\/em>) \u2013 5 = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 2<em>q <\/em>+ 8 \u2212 8<em>q <\/em>\u2013 5 = 0<\/p>\n<p style=\"text-align: justify;\">\u21d2 \u22126<em>q <\/em>= \u22123\u21d2 <em>q <\/em>= \u00bd<\/p>\n<p style=\"text-align: justify;\">Putting value of q in (p = 2 \u2013 2q), we get<\/p>\n<p style=\"text-align: justify;\"><em>p <\/em>= 2 \u2013 2 (\u00bd) = 2 \u2013 1 = 1<\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.6<\/p>\n<p style=\"text-align: justify;\">Putting values of p and q in (<img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image013.png\" \/>= <em>p<\/em> and <img decoding=\"async\" style=\"height: 44px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image014.png\" \/>= <em>q<\/em>), we get <em>x <\/em>= 1 and <em>y <\/em>= 2<\/p>\n<p style=\"text-align: justify;\"><strong>(vii)<\/strong> <img decoding=\"async\" style=\"height: 44px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image009.png\" \/> \u2026 (1)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image010.png\" \/> \u2026(2)<\/p>\n<p style=\"text-align: justify;\">Let <img decoding=\"async\" style=\"height: 44px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting this in (1) and (2), we get<\/p>\n<p style=\"text-align: justify;\">10<em>p <\/em>+ 2<em>q <\/em>= 4 \u2026 (3)<\/p>\n<p style=\"text-align: justify;\">15<em>p <\/em>\u2212 5<em>q <\/em>= \u22122 \u2026 (4)<\/p>\n<p style=\"text-align: justify;\">From equation (3),<\/p>\n<p style=\"text-align: justify;\">2<em>q <\/em>= 4 \u2212 10<em>p<\/em><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>q <\/em>= 2 \u2212 5<em>p \u2026 <\/em>(5)<\/p>\n<p style=\"text-align: justify;\">Putting this in (4), we get<\/p>\n<p style=\"text-align: justify;\">15<em>p <\/em>\u2013 5 (2 \u2212 5<em>p<\/em>) = \u22122<\/p>\n<p style=\"text-align: justify;\">\u21d2 15<em>p <\/em>\u2013 10 + 25<em>p <\/em>= \u22122<\/p>\n<p style=\"text-align: justify;\">\u21d2 40<em>p <\/em>= 8\u21d2 <em>p <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting value of p in (5), we get<\/p>\n<p style=\"text-align: justify;\"><em>q <\/em>= 2 \u2013 5 (<img decoding=\"async\" style=\"height: 42px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image029.png\" \/>) = 2 \u2013 1 = 1<\/p>\n<p style=\"text-align: justify;\">Putting values of p and q in (<img decoding=\"async\" style=\"height: 44px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image037.png\" \/>), we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image038.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>+ <em>y <\/em>= 5 \u2026 (6) and <em>x <\/em>\u2013 <em>y <\/em>= 1 \u2026 (7)<\/p>\n<p style=\"text-align: justify;\">Adding (6) and (7), we get<\/p>\n<p style=\"text-align: justify;\">2<em>x <\/em>= 6 \u21d2 <em>x <\/em>= 3<\/p>\n<p style=\"text-align: justify;\">Putting <em>x <\/em>= 3 in (7), we get<\/p>\n<p style=\"text-align: justify;\">3 \u2013 <em>y <\/em>= 1<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>y <\/em>= 3 \u2013 1 = 2<\/p>\n<p style=\"text-align: justify;\">Therefore, <em>x <\/em>= 3 and <em>y <\/em>= 2<\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.6<\/p>\n<p style=\"text-align: justify;\"><strong>(viii)<\/strong> <img decoding=\"async\" style=\"height: 44px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image011.png\" \/> \u2026 (1)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 174px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image012.png\" \/> \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">Let <img decoding=\"async\" style=\"height: 44px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image039.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting this in (1) and (2), we get<\/p>\n<p style=\"text-align: justify;\"><em>p <\/em>+ <em>q <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image040.png\" \/> and <img decoding=\"async\" style=\"height: 42px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image041.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 4<em>p <\/em>+ 4<em>q <\/em>= 3 \u2026 (3) and 4<em>p <\/em>\u2212 4<em>q <\/em>= \u22121 \u2026 (4)<\/p>\n<p style=\"text-align: justify;\">Adding (3) and (4), we get<\/p>\n<p style=\"text-align: justify;\">8<em>p <\/em>= 2 \u21d2 <em>p <\/em>= \u00bc<\/p>\n<p style=\"text-align: justify;\">Putting value of p in (3), we get<\/p>\n<p style=\"text-align: justify;\">4 (\u00bc) + 4<em>q <\/em>= 3<\/p>\n<p style=\"text-align: justify;\">\u21d2 1 + 4<em>q <\/em>= 3<\/p>\n<p style=\"text-align: justify;\">\u21d2 4<em>q <\/em>= 3 \u2013 1 = 2<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>q <\/em>= \u00bd<\/p>\n<p style=\"text-align: justify;\">Putting value of p and q in <img decoding=\"async\" style=\"height: 44px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image039.png\" \/>, we get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 170px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image042.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 3<em>x <\/em>+ <em>y <\/em>= 4 \u2026 (5) and 3<em>x <\/em>\u2013 <em>y <\/em>= 2 \u2026 (6)<\/p>\n<p style=\"text-align: justify;\">Adding (5) and (6), we get<\/p>\n<p style=\"text-align: justify;\">6<em>x <\/em>= 6 \u21d2 <em>x <\/em>= 1<\/p>\n<p style=\"text-align: justify;\">Putting <em>x <\/em>= 1 in (5) , we get<\/p>\n<p style=\"text-align: justify;\">3 (1) + <em>y <\/em>= 4<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>y <\/em>= 4 \u2013 3 = 1<\/p>\n<p style=\"text-align: justify;\">Therefore, <em>x <\/em>= 1 and <em>y <\/em>= 1<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.6<\/p>\n<h6><span class=\"ez-toc-section\" id=\"2_Formulate_the_following_problems_as_a_part_of_equations_and_hence_find_their_solutions\"><\/span><strong>2. Formulate the following problems as a part of equations, and hence find their solutions.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<\/div>\n<div>\n<p style=\"text-align: justify;\"><strong>(i) Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days.Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i) <\/strong>Let speed of rowing in still water = <em>x<\/em> km\/h<\/p>\n<p style=\"text-align: justify;\">Let speed of current = <em>y<\/em> km\/h<\/p>\n<p style=\"text-align: justify;\">So, speed of rowing downstream = (<em>x <\/em>+ <em>y<\/em>) km\/h<\/p>\n<p style=\"text-align: justify;\">And, speed of rowing upstream = (<em>x <\/em>\u2212 <em>y<\/em>) km\/h<\/p>\n<p style=\"text-align: justify;\">According to given conditions,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 150px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image043.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 2<em>x <\/em>+ 2<em>y <\/em>= 20 and 2<em>x <\/em>\u2212 2<em>y <\/em>= 4<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>+ <em>y <\/em>= 10 \u2026 (1) and <em>x <\/em>\u2013 <em>y <\/em>= 2 \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">Adding (1) and (2), we get<\/p>\n<p style=\"text-align: justify;\">2<em>x <\/em>= 12\u21d2 <em>x <\/em>= 6<\/p>\n<p style=\"text-align: justify;\">Putting <em>x <\/em>= 6 in (1), we get<\/p>\n<p style=\"text-align: justify;\">6 + <em>y <\/em>= 10<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>y <\/em>= 10 \u2013 6 = 4<\/p>\n<p style=\"text-align: justify;\">Therefore, speed of rowing in still water = 6 km\/h<\/p>\n<p style=\"text-align: justify;\">Speed of current = 4 km\/h<\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.6<\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>Let time taken by 1 woman alone to finish the work = <em>x<\/em> days<\/p>\n<p style=\"text-align: justify;\">Let time taken by 1 man alone to finish the work = <em>y<\/em> days<\/p>\n<p style=\"text-align: justify;\">So, 1 woman\u2019s 1-day work = (<img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image013.png\" \/>)<em>th<\/em> part of the work<\/p>\n<p style=\"text-align: justify;\">And, 1 man\u2019s 1-day work = (<img decoding=\"async\" style=\"height: 44px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image014.png\" \/>)<em>th<\/em> part of the work<\/p>\n<p style=\"text-align: justify;\">So, 2 women\u2019s 1-day work = (<img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image044.png\" \/>)<em>th<\/em> part of the work<\/p>\n<p style=\"text-align: justify;\">And, 5 men\u2019s 1-day work = (<img decoding=\"async\" style=\"height: 44px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image045.png\" \/>)<em>th<\/em> part of the work<\/p>\n<p style=\"text-align: justify;\">Therefore, 2 women and 5 men\u2019s 1-day work = (<img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image044.png\" \/>+<img decoding=\"async\" style=\"height: 44px; width: 18px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image045.png\" \/>)<em>th<\/em> part of the work\u2026 (1)<\/p>\n<p style=\"text-align: justify;\">It is given that 2 women and 5 men complete work in = 4 days<\/p>\n<p style=\"text-align: justify;\">It means that in 1 day, they will be completing <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image046.png\" \/><em>th<\/em> part of the work \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">Clearly, we can see that (1) = (2)<\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 44px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image047.png\" \/> \u2026 (3)<\/p>\n<p style=\"text-align: justify;\">Similarly, <img decoding=\"async\" style=\"height: 44px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image048.png\" \/> \u2026 (4)<\/p>\n<p style=\"text-align: justify;\">Let <img decoding=\"async\" style=\"height: 44px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image049.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting this in (3) and (4), we get<\/p>\n<p style=\"text-align: justify;\">2<em>p <\/em>+ 5<em>q <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image046.png\" \/> and 3<em>p <\/em>+ 6<em>q <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image022.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 8<em>p <\/em>+ 20<em>q <\/em>= 1 \u2026 (5) and 9<em>p <\/em>+ 18<em>q <\/em>= 1 \u2026 (6)<\/p>\n<p style=\"text-align: justify;\">Multiplying (5) by 9 and (6) by 8, we get<\/p>\n<p style=\"text-align: justify;\">72<em>p <\/em>+ 180<em>q <\/em>= 9 \u2026 (7)<\/p>\n<p style=\"text-align: justify;\">72<em>p <\/em>+ 144<em>q <\/em>= 8 \u2026 (8)<\/p>\n<p style=\"text-align: justify;\">Subtracting (8) from (7), we get<\/p>\n<p style=\"text-align: justify;\">36<em>q <\/em>= 1\u21d2 <em>q <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image050.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting this in (6), we get<\/p>\n<p style=\"text-align: justify;\">9<em>p <\/em>+ 18 (<img decoding=\"async\" style=\"height: 42px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image050.png\" \/>) = 1<\/p>\n<p style=\"text-align: justify;\">\u21d2 9<em>p <\/em>= \u00bd\u21d2 p = <img decoding=\"async\" style=\"height: 42px; width: 22px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image051.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting values of p and q in <img decoding=\"async\" style=\"height: 44px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image049.png\" \/>, we get <em>x <\/em>= 18 and <em>y <\/em>= 36<\/p>\n<p style=\"text-align: justify;\">Therefore, 1 woman completes work in = 18 days<\/p>\n<p style=\"text-align: justify;\">And, 1 man completes work in = 36 days<\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.6<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> Let speed of train = <em>x<\/em> km\/h and let speed of bus = <em>y<\/em> km\/h<\/p>\n<p style=\"text-align: justify;\">According to given conditions,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 239px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image052.png\" \/><\/p>\n<p style=\"text-align: justify;\">Let <img decoding=\"async\" style=\"height: 44px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image049.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting this in the above equations, we get<\/p>\n<p style=\"text-align: justify;\">60<em>p <\/em>+ 240<em>q <\/em>= 4 \u2026 (1)<\/p>\n<p style=\"text-align: justify;\">And 100<em>p <\/em>+ 200<em>q <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image053.png\" \/> \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">Multiplying (1) by 5 and (2) by 3, we get<\/p>\n<p style=\"text-align: justify;\">300<em>p <\/em>+ 1200<em>q <\/em>= 20 \u2026 (3)<\/p>\n<p style=\"text-align: justify;\">300<em>p <\/em>+ 600<em>q <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image054.png\" \/> \u2026 (4)<\/p>\n<p style=\"text-align: justify;\">Subtracting (4) from (3), we get<\/p>\n<p style=\"text-align: justify;\">600<em>q <\/em>= 20 \u2212 <img decoding=\"async\" style=\"height: 42px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image054.png\" \/>= 7.5<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>q <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image055.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting value of q in (2), we get<\/p>\n<p style=\"text-align: justify;\">100<em>p <\/em>+ 200 (<img decoding=\"async\" style=\"height: 42px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image055.png\" \/>) = <img decoding=\"async\" style=\"height: 42px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image053.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 100<em>p <\/em>+ 2.5 = <img decoding=\"async\" style=\"height: 42px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image053.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 100<em>p <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image053.png\" \/>\u2013 2.5<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>p <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image056.png\" \/><\/p>\n<p style=\"text-align: justify;\">But <img decoding=\"async\" style=\"height: 44px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image049.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, <em>x <\/em>=<img decoding=\"async\" style=\"height: 42px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image057.png\" \/>km\/h and <em>y <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.6\/image058.png\" \/>km\/h<\/p>\n<p style=\"text-align: justify;\">Therefore, speed of train = 60 km\/h<\/p>\n<p style=\"text-align: justify;\">And, speed of bus = 80 km\/h<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Exercise_36\"><\/span>NCERT Solutions for Class 10 Maths Exercise 3.6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 10 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 10 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 10 Maths have total 15 chapters. 10 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 10 solutions PDF and Maths ncert class 10 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.<\/p>\n<h5 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"_Download_CBSE_Question_Paper_2018\"><\/span><b><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-question-paper-2018-for-class-10-12\/\">\u00a0Download CBSE Question Paper 2018<\/a><\/strong><\/b><span class=\"ez-toc-section-end\"><\/span><\/h5>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_app_for_Class_10\"><\/span>CBSE app for Class 10<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 10 Maths, Computer Science, Home Science,Hindi ,English, Social Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Exercise 3.6 Class 10 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class &#8230; <a title=\"NCERT Solutions for Class 10 Maths Exercise 3.6\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-6\/\" aria-label=\"More on NCERT Solutions for Class 10 Maths Exercise 3.6\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":30002,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1347,281],"tags":[1042,283,321,1485,216],"class_list":["post-4917","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","category-ncert-solutions","tag-cbse-class-10-mathematics","tag-cbse-study-material","tag-mathematics","tag-maths","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 10 Maths Exercise 3.6 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 10 Maths Exercise 3.6 in PDF format for free download. 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