Question

615 coins consist of one rupee, 50 paise and 25 paise coins. Their values are in the ratio of 3 : 5 : 7, respectively. Find the number of 50 paise coins.

• A. 150
• B. 180
• C. 160
• D. 170

Answer 1

Answer:

A. 150

Given: 615 coins consist of one rupee, 50 paise and 25 paise coins. Their values are in the ratio of 3 : 5 : 7. Calculation: Let number of coins of 1 rupee, 50 Paise and 25 Paise be M, N and P respectively ⇒ M + N + P = 615 Also, ⇒ 100M ∶ 50N ∶ 25P = 3 ∶ 5 ∶ 7 Let ⇒ M ∶ N ∶ P = K Then, ⇒ M = 3K/100, N = 5K/50, P = 7K/25 According to question, ⇒ (3K/100) + (5K/50) + (7K/25) = 615 ⇒ 3K + 10K + 28K = 61500 ⇒ 41K = 61500 ⇒ K = 1500 ∴ Number of 50 Paise coins = 5K/50 = (1500 × 5)/50 = 150 Therefore the number of 50 paise coins is 150. Shortcut Trick Coins value = Rs. 1, Rs. 0.50(50 paise), Rs. 0.25 (25 paise) Coins are required in a ratio = 1 : 2 : 4 ....(1) [For equal value] Their values are in the ratio = 3 : 5 : 7 .....(2) So Number of coins = (1) × (2) ratio of number of coins = 3 : 10 : 28 So 3x + 10x + 28x = 615 x = 15 So 50 paise coins = 10x = 15 × 10 = 150