A bag contains Rs 750 in the form of rupees , 50 P and 25 P coins in the ratio `5 : 8 : 4`. Find the number of coins of each type.

Answer

To solve the problem, we need to find the number of coins of each type (rupee coins, 50 paisa coins, and 25 paisa coins) given that they are in the ratio of 5:8:4 and their total value is Rs 750.

### Step-by-Step Solution:

1. **Understand the Ratios**:
The ratio of the number of coins is given as 5:8:4. Let's denote:
- Number of Rupee coins = 5x
- Number of 50 P coins = 8x
- Number of 25 P coins = 4x

2. **Convert the Values**:
We need to express the total value of these coins in the same unit (paisa) for easier calculation.
- 1 Rupee = 100 Paisa
- Therefore, the value of each type of coin in paisa is:
- Value of Rupee coins = 5x * 100 = 500x paisa
- Value of 50 P coins = 8x * 50 = 400x paisa
- Value of 25 P coins = 4x * 25 = 100x paisa

3. **Set Up the Equation**:
The total value of all the coins is Rs 750, which is equal to 750 * 100 = 75000 paisa.
Therefore, we can set up the equation:
\( 500x + 400x + 100x = 75000 \)

4. **Combine Like Terms**:
Combine the terms on the left side:
\( 1000x = 75000 \)

5. **Solve for x**:
Divide both sides by 1000:
\( x = \frac{75000}{1000} = 75 \)

6. **Find the Number of Coins**:
Now substitute the value of x back to find the number of coins:
- Number of Rupee coins = 5x = 5 * 75 = 375
- Number of 50 P coins = 8x = 8 * 75 = 600
- Number of 25 P coins = 4x = 4 * 75 = 300

### Final Answer:
- Number of Rupee coins = 375
- Number of 50 P coins = 600
- Number of 25 P coins = 300