Question

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. $14 \dfrac{2}{7}\%$
• C. 10%
• D. 30%

Hint:

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.

Answer 1

The Correct Option is B

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). \[ \boxed{10\%} \]