Q.4 The number of coins of ₹1, ₹5, and ₹10 denominations that a person has are in the
ratio 5:3:13. Of the total amount, the percentage of money in ₹5 coins is
(A) 21%
(B) 14 2/7%
(C) 10%
(D) 30%
This GATE 2024 aptitude question asks for the percentage of the
total money contributed by ₹5 coins.
Problem Breakdown
Let the common multiple of the ratio be k.
- Number of ₹1 coins = 5k
- Number of ₹5 coins = 3k
- Number of ₹10 coins = 13k
Value Contribution from Each Coin Type
₹1 coins: 5k × 1 = 5k
₹5 coins: 3k × 5 = 15k
₹10 coins: 13k × 10 = 130k
Total Amount
Total money = 5k + 15k + 130k = 150k
Percentage of Money from ₹5 Coins
Percentage =
(15k / 150k) × 100% = 10%
Options Analysis
| Option | Value | Explanation | Correct? |
|---|---|---|---|
| (A) | 21% | Calculates percentage of number of coins: 3 / (5 + 3 + 13) × 100%. Ignores coin values. |
No |
| (B) | 14 2/7% | Uses incorrect total (107) and mishandles ₹1 coin value. | No |
| (C) | 10% | Correctly uses money contribution: (15k / 150k) × 100%. |
Yes |
| (D) | 30% | Considers only ₹1 and ₹5 coins, ignores ₹10 coins. | No |
Final Answer
The correct answer is (C): 10%
