Chapter 2 (2.2) questions:-15,16

Que no 14

Ex 2.2 Class 8 Maths Question 16. The organisers of an essay competition decide that a winner in the competition gets a prize of ₹ 100 and a participant who does not win gets a prize of ₹ 25. The total prize money distributed is ₹ 3,000. Find the number of winners, if the total number of participants is 63. Solution: Let the number of winners = x Number of participants who does not win the prize = (63 – x) Amount got by winners = ₹ 100 × x = ₹ 100x Amount got by loosers = ₹ (63 – x) × 25 = ₹ (1575 – 25x) As per the conditions, we get 100x + 1575 – 25x = 3000 ⇒ 75x + 1575 = 3000 ⇒ 75x = 3000 – 1575 (transposing 1575 to RHS) ⇒ 75x = 1425 ⇒ x = 1425 ÷ 75 (Transposing 75 to RHS)  ⇒ x = 19 Thus, the number of winners = 19

Ex 2.2 Class 8 Maths Question 15. I have a total of ₹ 300 in coins of denomination ₹ 1, ₹ 2 and ₹ 5. The number of ₹ 2 coins is 3 times the number of ₹ 5 coins. The total number of coins is 160. How many coins of each denomination are with me? Solution: Let the number of ₹ 5 coins be x. Number of ₹ 2 coins = 3x Total number of coins = 160 Number of ₹ 1 coin = 160 – (x + 3x) = 160 – 4x Converting the number of coins into rupees, we have x coins of ₹ 5 amount to ₹ 5x 3x coins of ₹ 2 amount to ₹ 3x × 2 = ₹ 6x and (160 – 4x) coins of ₹ 1 amount to ₹ 1 × (160 – 4x) = ₹ (160 – 4x) As per the conditions, we have 5x + 6x + 160 – 4x = 300 ⇒ 7x + 160 = 300 ⇒ 7x = 300 – 160 (transposing 160 to RHS) ⇒ 7x = 140 ⇒ x = 140 ÷ 7 (transposing 7 to RHS) ⇒ x = 20 Thus, number of ₹ 5 coins = 20 Number of ₹ 2 coins = 3 × 20 = 60 and Number of ₹ 1 coins = 160 – 4 × 20 = 160 – 80 = 80