A bag contains ₹1, 50-paise and 25-paise coins. The total values contributed…
2021
A bag contains ₹1, 50-paise and 25-paise coins. The total values contributed by the ₹1, 50-paise and 25-paise coins are in the ratio 5 : 2 : 3, respectively. If the total number of coins is 420, what is the total value of all the coins?
Answer: A. 200 — ConceptWhen coins of different denominations together make up a given value ratio, the ratio of value is NOT the same as the ratio of coin counts. The number…
- A.
200
- B.
180
- C.
220
- D.
160
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Show answer & explanation
Correct answer: A
Concept
When coins of different denominations together make up a given value ratio, the ratio of value is NOT the same as the ratio of coin counts. The number of coins of each denomination equals that denomination's total value divided by its face value (₹1, ₹0.50, ₹0.25). So a value ratio must first be converted into a coin-count ratio before using any condition stated on the number of coins.
Application
Let the value ratio parts be 5x, 2x and 3x rupees for the ₹1, 50 paise and 25 paise coins respectively (ratio 5 : 2 : 3).
Number of ₹1 coins = value ÷ face value = 5x ÷ 1 = 5x.
Number of 50 paise (₹0.50) coins = 2x ÷ 0.50 = 4x.
Number of 25 paise (₹0.25) coins = 3x ÷ 0.25 = 12x.
Total number of coins = 5x + 4x + 12x = 21x, and this equals the given total, 420, so 21x = 420, giving x = 20.
Total value of all coins = 5x + 2x + 3x = 10x = 10 × 20 = ₹200.
Cross-check
With x = 20, there are 100 coins of ₹1 (value ₹100), 80 coins of 50 paise (value ₹40), and 240 coins of 25 paise (value ₹60). These add to 100 + 80 + 240 = 420 coins, matching the given total, and the values 100 : 40 : 60 simplify to 5 : 2 : 3, matching the given ratio. The total value ₹100 + ₹40 + ₹60 = ₹200 confirms the answer.