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
Options:
(A) 21%
(B) 14
2
7%
(C) 10%
(D) 30%
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2024 Q.4)**
**1. Governing Concept**:
- **Topic**: Numerical Ability & Ratio-to-Percentage Computation
- Ratio of number of coins of ₹1, ₹5, ₹10 is $5 : 3 : 13$.
- Let coin counts be $5k, 3k, 13k$.
- Value from ₹1 coins: $5k \times 1 = 5k$
- Value from ₹5 coins: $3k \times 5 = 15k$
- Value from ₹10 coins: $13k \times 10 = 130k$
- Total monetary amount: $5k + 15k + 130k = 150k$.
- Percentage contribution of ₹5 coins:
$\text{Percentage} = \frac{15k}{150k} \times 100\% = 10\%$
**2. Option Analysis**:
- **Option (A) [21%] is INCORRECT**: Arithmetic miscalculation based on coin counts rather than monetary value.
- **Option (B) [14 2/7%] is INCORRECT**: Corresponds to $\frac{3}{5+3+13} = \frac{3}{21} = \frac{1}{7} \approx 14.28\%$, which is the coin *count* percentage, not amount.
- **Option (C) [10%] is CORRECT**: Directly derived as $\frac{15}{150} \times 100\% = 10\%$.
- **Option (D) [30%] is INCORRECT**: Erroneous ratio multiplier.
**3. Final Answer**:
- **Correct Choice**: **C**
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