{"id":4919,"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-3-5\/"},"modified":"2023-03-22T15:18:05","modified_gmt":"2023-03-22T09:48:05","slug":"ncert-solutions-for-class-10-maths-exercise-3-5","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-5\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Exercise 3.5"},"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-3-5\/#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-3-5\/#1_Which_of_the_following_pairs_of_linear_equations_has_unique_solution_no_solution_or_infinitely_many_solutions_In_case_there_is_a_unique_solution_find_it_by_using_cross_multiplication_method\" >1. Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.<\/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-3-5\/#Herethis_means_that_there_is_unique_solution_for_the_given_equations\" >Herethis means that there is unique solution for the given equations.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-5\/#2_i_For_which_values_of_a_and_b_does_the_following_pair_of_linear_equations_have_an\" >2. (i) For which values of a and b does the following pair of linear equations have an<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-5\/#Linear_equations_have_infinite_many_solutions_if\" >Linear equations have infinite many solutions if<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-5\/#3_Solve_the_following_pair_of_linear_equations_by_the_substitution_and_cross-multiplication_methods\" >3. Solve the following pair of linear equations by the substitution and cross-multiplication methods:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-5\/#Cross_multiplication_method\" >Cross multiplication method<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-5\/#4_Form_the_pair_of_linear_equations_in_the_following_problems_and_find_their_solutions_if_they_exist_by_any_algebraic_method\" >4. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:<\/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-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-5\/#NCERT_Solutions_for_Class_10_Maths_Exercise_35\" >NCERT Solutions for Class 10 Maths Exercise 3.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-5\/#CBSE_app_for_Class_10\" >CBSE app for Class 10<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 10 Maths Exercise 3.5 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 3.5\" width=\"189\" height=\"233\" \/><\/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_Which_of_the_following_pairs_of_linear_equations_has_unique_solution_no_solution_or_infinitely_many_solutions_In_case_there_is_a_unique_solution_find_it_by_using_cross_multiplication_method\"><\/span><strong>1. Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) x \u2013 3y \u2013 3 = 0 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>3x \u2013 9y \u2013 2 = 0 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)2<em>x <\/em>+ <em>y <\/em>= 5<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>3<em>x <\/em>+ 2<em>y <\/em>= 8<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) 3<em>x <\/em>\u2212 5<em>y <\/em>= 20 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>6<em>x <\/em>\u2212 10<em>y <\/em>= 40 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <em>x <\/em>\u2212 3<em>y <\/em>\u2013 7 = 0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>3<em>x <\/em>\u2212 3<em>y <\/em>\u2013 15 = 0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i) <\/strong><em>x <\/em>\u2212 3<em>y <\/em>\u2013 3 = 0<\/p>\n<p style=\"text-align: justify;\">3<em>x <\/em>\u2212 9<em>y <\/em>\u2013 2 = 0<\/p>\n<p style=\"text-align: justify;\">Comparing equation <em>x <\/em>\u2212 3<em>y <\/em>\u2013 3 = 0 with <em>a<\/em><sub>1<\/sub><em>x <\/em>+<em>b<\/em><sub>1<\/sub><em>y <\/em>+ <em>c<\/em><sub>1<\/sub> = 0 and 3<em>x <\/em>\u2212 9<em>y <\/em>\u2013 2 = 0 with <img decoding=\"async\" style=\"height: 24px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image001.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">We get <img decoding=\"async\" style=\"height: 24px; width: 166px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image002.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 170px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\">Here <img decoding=\"async\" style=\"height: 45px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image004.png\" \/>this means that the two lines are parallel.<\/p>\n<p style=\"text-align: justify;\">Therefore, there is no solution for the given equations i.e. it is inconsistent.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>2<em>x <\/em>+ <em>y <\/em>= 5<\/p>\n<p style=\"text-align: justify;\">3<em>x <\/em>+ 2<em>y <\/em>= 8<\/p>\n<p style=\"text-align: justify;\">Comparing equation 2<em>x <\/em>+ <em>y <\/em>= 5 with <img decoding=\"async\" style=\"height: 24px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image005.png\" \/> and 3<em>x <\/em>+ 2<em>y <\/em>= 8 with <img decoding=\"async\" style=\"height: 24px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image001.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">We get <img decoding=\"async\" style=\"height: 24px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image006.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image007.png\" \/><\/p>\n<h6><span class=\"ez-toc-section\" id=\"Herethis_means_that_there_is_unique_solution_for_the_given_equations\"><\/span>Here<img decoding=\"async\" style=\"height: 45px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image008.png\" \/>this means that there is unique solution for the given equations.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 8\" style=\"height: 80px; width: 163px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image009.jpg\" alt=\"1\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 319px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image010.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 42px; width: 174px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image011.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image012.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image013.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= 2 and <em>y <\/em>= 1<\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.5<\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <\/strong>3<em>x <\/em>\u2212 5<em>y <\/em>= 20<\/p>\n<p style=\"text-align: justify;\">6<em>x <\/em>\u2212 10<em>y <\/em>= 40<\/p>\n<p style=\"text-align: justify;\">Comparing equation 3<em>x <\/em>\u2212 5<em>y <\/em>= 20 with <em><img decoding=\"async\" style=\"height: 24px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image005.png\" \/><\/em>and 6<em>x <\/em>\u2212 10<em>y <\/em>= 40 with <img decoding=\"async\" style=\"height: 24px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image001.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">We get <img decoding=\"async\" style=\"height: 24px; width: 178px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image014.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 186px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image015.png\" \/><\/p>\n<p style=\"text-align: justify;\">Here <img decoding=\"async\" style=\"height: 45px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image016.png\" \/><\/p>\n<p style=\"text-align: justify;\">It means lines coincide with each other.<\/p>\n<p style=\"text-align: justify;\">Hence, there are infinite many solutions.<\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <\/strong><em>x <\/em>\u2212 3<em>y <\/em>\u2013 7 = 0<\/p>\n<p style=\"text-align: justify;\">3<em>x <\/em>\u2212 3<em>y <\/em>\u2013 15 = 0<\/p>\n<p style=\"text-align: justify;\">Comparing equation <em>x <\/em>\u2212 3<em>y <\/em>\u2013 7 = 0 with <em><img decoding=\"async\" style=\"height: 24px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image005.png\" \/><\/em> and 3<em>x <\/em>\u2212 3<em>y <\/em>\u2013 15 = 0 with <img decoding=\"async\" style=\"height: 24px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image001.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">We get <img decoding=\"async\" style=\"height: 24px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image017.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 176px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image018.png\" \/><\/p>\n<p style=\"text-align: justify;\">Here <img decoding=\"async\" style=\"height: 45px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image008.png\" \/>this means that we have unique solution for these equations.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 7\" style=\"height: 94px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image019.jpg\" alt=\"1\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 370px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image020.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 42px; width: 184px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image021.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 42px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image022.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= 4 and <em>y <\/em>= \u20131<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_i_For_which_values_of_a_and_b_does_the_following_pair_of_linear_equations_have_an\"><\/span><strong>2. (i) For which values of a and b does the following pair of linear equations have an <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>infinite number of solutions? <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>2<em>x <\/em>+ 3<em>y <\/em>= 7<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(<em>a <\/em>\u2212 <em>b<\/em>) <em>x <\/em>+ (<em>a <\/em>+ <em>b<\/em>) <em>y <\/em>= 3<em>a <\/em>+ <em>b <\/em>\u2013 2<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) For which value of k will the following pair of linear equations have no <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>solution?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>3<em>x <\/em>+ <em>y <\/em>= 1<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(2<em>k <\/em>\u2212 1) <em>x <\/em>+ (<em>k <\/em>\u2212 1) <em>y <\/em>= 2<em>k <\/em>+ 1<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Comparing equation 2<em>x <\/em>+ 3<em>y <\/em>\u2013 7 = 0 with <img decoding=\"async\" style=\"height: 24px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image005.png\" \/> and (<em>a <\/em>\u2212 <em>b<\/em>) <em>x <\/em>+ (<em>a <\/em>+ <em>b<\/em>)<\/p>\n<p style=\"text-align: justify;\"><em>y <\/em>\u2212 3<em>a <\/em>\u2013 <em>b <\/em>+ 2 = 0 with <img decoding=\"async\" style=\"height: 24px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image001.png\" \/><\/p>\n<p style=\"text-align: justify;\">We get <img decoding=\"async\" style=\"height: 24px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image023.png\" \/>and <img decoding=\"async\" style=\"height: 26px; width: 209px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image024.png\" \/> and <img decoding=\"async\" style=\"height: 24px; width: 110px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image025.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Linear_equations_have_infinite_many_solutions_if\"><\/span>Linear equations have infinite many solutions if <img decoding=\"async\" style=\"height: 45px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image016.png\" \/><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 41px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 41px; width: 227px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 2<em>a <\/em>+ 2<em>b <\/em>= 3<em>a <\/em>\u2212 3<em>b <\/em>and 6 \u2212 3<em>b <\/em>\u2212 9<em>a <\/em>= \u22127<em>a <\/em>\u2212 7<em>b<\/em><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>a <\/em>= 5<em>b\u2026 <\/em>(1) and \u22122<em>a <\/em>= \u22124<em>b <\/em>\u2013 6\u2026 (2)<\/p>\n<p style=\"text-align: justify;\">Putting (1) in (2), we get<\/p>\n<p style=\"text-align: justify;\">\u22122 (5<em>b<\/em>) = \u22124<em>b <\/em>\u2013 6<\/p>\n<p style=\"text-align: justify;\">\u21d2 \u221210<em>b <\/em>+ 4<em>b <\/em>= \u22126<\/p>\n<p style=\"text-align: justify;\">\u21d2 \u22126<em>b <\/em>= \u20136 \u21d2 <em>b <\/em>= 1<\/p>\n<p style=\"text-align: justify;\">Putting value of b in (1), we get<\/p>\n<p style=\"text-align: justify;\"><em>a <\/em>= 5<em>b <\/em>= 5 (1) = 5<\/p>\n<p style=\"text-align: justify;\">Therefore, <em>a <\/em>= 5 and <em>b <\/em>= 1<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Comparing (3<em>x <\/em>+ <em>y <\/em>\u2013 1 = 0) with <img decoding=\"async\" style=\"height: 24px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image005.png\" \/> and (2<em>k <\/em>\u2212 1)<em>x <\/em>+ (<em>k <\/em>\u2212 1)<em>y <\/em>\u22122<em>k <\/em>\u2013 1 = 0) with <img decoding=\"async\" style=\"height: 24px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image001.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">We get <img decoding=\"async\" style=\"height: 24px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image028.png\" \/> and <img decoding=\"async\" style=\"height: 26px; width: 209px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image029.png\" \/> and <em>c<\/em><sub>2<\/sub> = \u22122<em>k <\/em>\u2212 1<\/p>\n<p style=\"text-align: justify;\">Linear equations have no solution if <img decoding=\"async\" style=\"height: 45px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 41px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image030.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 41px; width: 90px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image031.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 3 (<em>k <\/em>\u2212 1) = 2<em>k <\/em>\u2013 1<\/p>\n<p style=\"text-align: justify;\">\u21d2 3<em>k <\/em>\u2013 3 = 2<em>k <\/em>\u2212 1<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>k <\/em>= 2<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Solve_the_following_pair_of_linear_equations_by_the_substitution_and_cross-multiplication_methods\"><\/span><strong>3. Solve the following pair of linear equations by the substitution and cross-multiplication methods:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>8<em>x <\/em>+ 5<em>y <\/em>= 9<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>3<em>x <\/em>+ 2<em>y <\/em>= 4<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. Substitution Method<\/strong><\/p>\n<p style=\"text-align: justify;\">8<em>x <\/em>+ 5<em>y <\/em>= 9 \u2026 <strong>(1)<\/strong><\/p>\n<p style=\"text-align: justify;\">3<em>x <\/em>+ 2<em>y <\/em>= 4 \u2026 <strong>(2)<\/strong><\/p>\n<p style=\"text-align: justify;\">From equation <strong>(1)<\/strong>,<\/p>\n<p style=\"text-align: justify;\">5<em>y <\/em>= 9 \u2212 8<em>x<\/em>\u21d2 <em>y <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image032.png\" \/><\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.5<\/p>\n<p style=\"text-align: justify;\">Putting this in equation <strong>(2)<\/strong>, we get<\/p>\n<p style=\"text-align: justify;\">3<em>x <\/em>+ 2 <img decoding=\"async\" style=\"height: 45px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image033.png\" \/>= 4<\/p>\n<p style=\"text-align: justify;\">\u21d2 3<em>x <\/em>+ <img decoding=\"async\" style=\"height: 42px; width: 58px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image034.png\" \/> = 4<\/p>\n<p style=\"text-align: justify;\">\u21d2 3<em>x <\/em>\u2212 <img decoding=\"async\" style=\"height: 42px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image035.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 15<em>x <\/em>\u2212 16<em>x <\/em>= 20 \u2013 18<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= \u22122<\/p>\n<p style=\"text-align: justify;\">Putting value of <strong>x<\/strong> in<strong> (1)<\/strong>, we get<\/p>\n<p style=\"text-align: justify;\">8 (\u22122) + 5<em>y <\/em>= 9<\/p>\n<p style=\"text-align: justify;\">\u21d2 5<em>y <\/em>= 9 + 16 = 25\u21d2 <em>y <\/em>= 5<\/p>\n<p style=\"text-align: justify;\">Therefore, <em>x <\/em>= \u22122 and <em>y <\/em>= 5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Cross_multiplication_method\"><\/span><strong>Cross multiplication method<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\">8<em>x <\/em>+ 5<em>y <\/em>= 9 \u2026 <strong>(1)<\/strong><\/p>\n<p style=\"text-align: justify;\">3<em>x <\/em>+ 2<em>y <\/em>= 4 \u2026 <strong>(2)<\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 6\" style=\"height: 112px; width: 262px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image036.jpg\" alt=\"3\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 44px; width: 281px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 42px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image038.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <img decoding=\"async\" style=\"height: 42px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image039.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= \u22122 and <em>y <\/em>= 5<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Form_the_pair_of_linear_equations_in_the_following_problems_and_find_their_solutions_if_they_exist_by_any_algebraic_method\"><\/span><strong>4. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) A fraction becomes <img decoding=\"async\" style=\"height: 42px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image040.png\" \/>when 1 is subtracted from the numerator and it becomes <img decoding=\"async\" style=\"height: 42px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image041.png\" \/> when 8 is added to its denominator. Find the fraction.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.(i)<\/strong>Let fixed monthly charge = Rs x and let charge of food for one day = Rs y<\/p>\n<p style=\"text-align: justify;\">According to given conditions,<\/p>\n<p style=\"text-align: justify;\"><em>x <\/em>+ 20<em>y <\/em>= 1000 \u2026 (1),<\/p>\n<p style=\"text-align: justify;\">and <em>x <\/em>+ 26<em>y <\/em>= 1180 \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">Subtracting equation (1) from equation (2), we get<\/p>\n<p style=\"text-align: justify;\">6<em>y <\/em>= 180<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>y <\/em>= 30<\/p>\n<p style=\"text-align: justify;\">Putting value of y in (1), we get<\/p>\n<p style=\"text-align: justify;\"><em>x <\/em>+ 20 (30) = 1000<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= 1000 \u2013 600 = 400<\/p>\n<p style=\"text-align: justify;\">Therefore, fixed monthly charges = Rs 400 and, charges of food for one day = Rs 30<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Let numerator = <em>x <\/em>and let denominator = <em>y<\/em><\/p>\n<p style=\"text-align: justify;\">According to given conditions,<\/p>\n<p style=\"text-align: justify;\"><em><img decoding=\"async\" style=\"height: 44px; width: 219px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image042.png\" \/><\/em><\/p>\n<p style=\"text-align: justify;\">\u21d2 3<em>x <\/em>\u2013 3 = <em>y \u2026 <\/em>(1) 4<em>x <\/em>= <em>y <\/em>+ 8 \u2026 (1)<\/p>\n<p style=\"text-align: justify;\">\u21d2 3<em>x <\/em>\u2013 <em>y <\/em>= 3 \u2026 (1) 4<em>x <\/em>\u2013 <em>y <\/em>= 8 \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">Subtracting equation (1) from (2), we get<\/p>\n<p style=\"text-align: justify;\">4<em>x <\/em>\u2013 <em>y <\/em>\u2212 (3<em>x <\/em>\u2212 <em>y<\/em>) = 8 \u2013 3<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= 5<\/p>\n<p style=\"text-align: justify;\">Putting value of x in (1), we get<\/p>\n<p style=\"text-align: justify;\">3 (5) \u2013 <em>y <\/em>= 3<\/p>\n<p style=\"text-align: justify;\">\u21d2 15 \u2013 <em>y <\/em>= 3<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>y <\/em>= 12<\/p>\n<p style=\"text-align: justify;\">Therefore, numerator = 5 and, denominator = 12<\/p>\n<p style=\"text-align: justify;\">It means fraction =<\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.5<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> Let number of correct answers = <em>x<\/em> and let number of wrong answers = <em>y<\/em><\/p>\n<p style=\"text-align: justify;\">According to given conditions,<\/p>\n<p style=\"text-align: justify;\">3<em>x <\/em>\u2013 <em>y <\/em>= 40 \u2026 (1)<\/p>\n<p style=\"text-align: justify;\">And, 4<em>x <\/em>\u2212 2<em>y <\/em>= 50 \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">From equation (1), <em>y <\/em>= 3<em>x <\/em>\u2212 40<\/p>\n<p style=\"text-align: justify;\">Putting this in (2), we get<\/p>\n<p style=\"text-align: justify;\">4<em>x <\/em>\u2013 2 (3<em>x <\/em>\u2212 40) = 50<\/p>\n<p style=\"text-align: justify;\">\u21d2 4<em>x <\/em>\u2212 6<em>x <\/em>+ 80 = 50<\/p>\n<p style=\"text-align: justify;\">\u21d2 \u22122<em>x <\/em>= \u221230<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= 15<\/p>\n<p style=\"text-align: justify;\">Putting value of x in (1), we get<\/p>\n<p style=\"text-align: justify;\">3 (15) \u2013 <em>y <\/em>= 40<\/p>\n<p style=\"text-align: justify;\">\u21d2 45 \u2013 <em>y <\/em>= 40<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>y <\/em>= 45 \u2013 40 = 5<\/p>\n<p style=\"text-align: justify;\">Therefore, number of correct answers = <em>x <\/em>= 15and number of wrong answers = <em>y <\/em>= 5<\/p>\n<p style=\"text-align: justify;\">Total questions = <em>x <\/em>+ <em>y <\/em>= 15 + 5 = 20<\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong>Let speed of car which starts from part A = x km\/hr<\/p>\n<p style=\"text-align: justify;\">Let speed of car which starts from part B = y km\/hr<\/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: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image044.png\" \/>(Assuming x &gt; y)<\/p>\n<p style=\"text-align: justify;\">\u21d2 5<em>x <\/em>\u2212 5<em>y <\/em>= 100<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>\u2013 <em>y <\/em>= 20 \u2026 (1)<\/p>\n<p style=\"text-align: justify;\">And, <img decoding=\"async\" style=\"height: 44px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image045.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>+ <em>y <\/em>= 100 \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>= 120<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= 60 km\/hr<\/p>\n<p style=\"text-align: justify;\">Putting value of x in (1), we get<\/p>\n<p style=\"text-align: justify;\">60 \u2013 <em>y <\/em>= 20<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>y <\/em>= 60 \u2013 20 = 40 km\/hr<\/p>\n<p style=\"text-align: justify;\">Therefore, speed of car starting from point A = 60 km\/hr<\/p>\n<p style=\"text-align: justify;\">And, Speed of car starting from point B = 40 km\/hr<\/p>\n<p style=\"text-align: justify;\"><strong>(v)<\/strong> Let length of rectangle = x units and Let breadth of rectangle = y units<\/p>\n<p style=\"text-align: justify;\">Area =<em>xy<\/em> square <em>units. <\/em>According to given conditions,<\/p>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 3.5<\/p>\n<p style=\"text-align: justify;\"><em>xy <\/em>\u2013 9 = (<em>x <\/em>\u2212 5) (<em>y <\/em>+ 3)<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>xy <\/em>\u2013 9 = <em>xy <\/em>+ 3<em>x <\/em>\u2212 5<em>y <\/em>\u2013 15<\/p>\n<p style=\"text-align: justify;\">\u21d2 3<em>x <\/em>\u2212 5<em>y <\/em>= 6 \u2026 (1)<\/p>\n<p style=\"text-align: justify;\">And, <em>xy <\/em>+ 67 = (<em>x <\/em>+ 3) (<em>y <\/em>+ 2)<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>xy <\/em>+ 67 = <em>xy <\/em>+ 2<em>x <\/em>+ 3<em>y <\/em>+ 6<\/p>\n<p style=\"text-align: justify;\">\u21d2 2<em>x <\/em>+ 3<em>y <\/em>= 61 \u2026 (2)<\/p>\n<p style=\"text-align: justify;\">From equation (1),<\/p>\n<p style=\"text-align: justify;\">3<em>x <\/em>= 6 + 5<em>y <\/em><\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= <img decoding=\"async\" style=\"height: 42px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image046.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting this in (2), we get<\/p>\n<p style=\"text-align: justify;\">2 <img decoding=\"async\" style=\"height: 45px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch03\/Ex3.5\/image047.png\" \/>+ 3<em>y <\/em>= 61<\/p>\n<p style=\"text-align: justify;\">\u21d2 12 + 10y + 9y = 183<\/p>\n<p style=\"text-align: justify;\">\u21d2 19<em>y <\/em>= 171<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>y <\/em>= 9 units<\/p>\n<p style=\"text-align: justify;\">Putting value of y in (2), we get<\/p>\n<p style=\"text-align: justify;\">2<em>x <\/em>+ 3 (9) = 61<\/p>\n<p style=\"text-align: justify;\">\u21d2 2<em>x <\/em>= 61 \u2013 27 = 34<\/p>\n<p style=\"text-align: justify;\">\u21d2 <em>x <\/em>= 17 units<\/p>\n<p style=\"text-align: justify;\">Therefore, length = 17 units and, breadth = 9 units<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Exercise_35\"><\/span>NCERT Solutions for Class 10 Maths Exercise 3.5<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<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","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Exercise 3.5 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 3.5\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-3-5\/\" aria-label=\"More on NCERT Solutions for Class 10 Maths Exercise 3.5\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":30004,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1347,281],"tags":[1042,283,438,321,1485,216],"class_list":["post-4919","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-class-10","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 3.5 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 10 Maths Exercise 3.5 in PDF format for free download. 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