A bag has ₹ 785 in the denomination of ₹ 2, ₹ 5 and ₹ 10 coins. The coins are in the ratio of 6 : 9 : 10. How many coins of ₹ 5 are in the bag?

Options

A. 60
B. 12
C. 45
D. 24

Answer

To solve the problem step by step, we can follow these instructions:

1. **Understand the Problem**: We have a total of ₹ 785 in coins of ₹ 2, ₹ 5, and ₹ 10, which are in the ratio of 6:9:10. We need to find out how many ₹ 5 coins are in the bag.

2. **Define Variables**: Let the number of ₹ 2 coins be \( 6x \), the number of ₹ 5 coins be \( 9x \), and the number of ₹ 10 coins be \( 10x \), where \( x \) is a common multiplier.

3. **Calculate Total Value of Coins**:
- The value contributed by ₹ 2 coins: \( 6x \times 2 = 12x \)
- The value contributed by ₹ 5 coins: \( 9x \times 5 = 45x \)
- The value contributed by ₹ 10 coins: \( 10x \times 10 = 100x \)

4. **Set Up the Equation**: The total value of all coins is given as ₹ 785. Therefore, we can set up the equation:
\[ 12x + 45x + 100x = 785 \]
Simplifying this gives:
\[ 157x = 785 \]

5. **Solve for \( x \)**:
\[ x = \frac{785}{157} = 5 \]

6. **Find the Number of ₹ 5 Coins**: Since the number of ₹ 5 coins is \( 9x \):
\[ 9x = 9 \times 5 = 45 \]

7. **Conclusion**: Therefore, the number of ₹ 5 coins in the bag is **45**.