A bag contains coins of Rs. 1, 50 paisa and 25 paisa in the ratio 7 : 8 : 12 respectively. If the total amount in the bag is Rs. 560, then the number of 25 paisa coins in the bag is :

Question

Accepted Answer

To determine the number of 25 paisa coins in the bag, we need to analyze the given information and use logical reasoning to support Option 3 as the correct answer.

### Explanation:

1. **Understanding the Ratios:**
   - The coins are in the ratio of Rs. 1 : 50 paisa : 25 paisa = 7 : 8 : 12.
   - Let the number of Rs. 1 coins be 7x, 50 paisa coins be 8x, and 25 paisa coins be 12x.

2. **Calculating the Total Value:**
   - The value of Rs. 1 coins = 7x * 1 = 7x rupees.
   - The value of 50 paisa coins = 8x * 0.50 = 4x rupees.
   - The value of 25 paisa coins = 12x * 0.25 = 3x rupees.

3. **Total Amount in the Bag:**
   - According to the problem, the total amount is Rs. 560.
   - Therefore, the equation becomes: 7x + 4x + 3x = 560.
   - Simplifying, we get: 14x = 560.

4. **Solving for x:**
   - Divide both sides by 14: x = 560 / 14 = 40.

5. **Finding the Number of 25 Paisa Coins:**
   - The number of 25 paisa coins is 12x.
   - Substituting the value of x: 12 * 40 = 480.

Thus, the number of 25 paisa coins in the bag is 480, which corresponds to Option 3.

### Why Other Options are Incorrect:

- **Option 1 (120 coins):** 
  - If there were 120 coins, then x would be 10 (since 12x = 120), leading to a total value of only Rs. 140, which is incorrect.

- **Option 2 (240 coins):**
  - If there were 240 coins, then x would be 20 (since 12x = 240), leading to a total value of Rs. 280, which is incorrect.

- **Option 4 (360 coins):**
  - If there were 360 coins, then x would be 30 (since 12x = 360), leading to a total value of Rs. 420, which is incorrect.

Therefore, the only correct option that satisfies the total amount of Rs. 560 is Option 3, with 480 coins of 25 paisa.