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 ?
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Always separate number of coins and value of coins. Here the ratio was given in number of coins, so converting to rupee values is essential before finding percentages.
21%
- $14 \dfrac{2}{7}\%$
10%
30%
The Correct Option is B
Solution and Explanation
Step 1: Represent the number of coins. Let the common ratio factor be $k$. Then: - Number of ₹1 coins = $5k$
- Number of ₹5 coins = $3k$
- Number of ₹10 coins = $13k$
Step 2: Find the value of money in each type. - Value of ₹1 coins = $5k \times 1 = 5k$
- Value of ₹5 coins = $3k \times 5 = 15k$
- Value of ₹10 coins = $13k \times 10 = 130k$
Step 3: Find the total money. \[ \text{Total} = 5k + 15k + 130k = 150k \]
Step 4: Find the percentage contribution of ₹5 coins. \[ \text{Percentage} = \frac{15k}{150k} \times 100 = \frac{15}{150} \times 100 = 10\% \] Wait this gives $10\%$, but the options include $14 \dfrac{2}{7}\%$. Let's carefully check.
Step 5: Re-evaluate. We must check whether the question asks for percentage of coins or percentage of value. - Number of coins ratio: $5:3:13$
- Value in rupees: $5k, 15k, 130k$
Total = $150k$ indeed.
\[ \frac{15k}{150k} \times 100 = 10\% \] So the correct calculation is $10\%$. That matches option (C), not (B). \[ \boxed{10\%} \]
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