A number of boys raised Rs.400 for a famine relief fund, each boy giving as many 25 paise coins as there were boys. The number of boys was :

Options

A. 40
B. 16
C. 20
D. 100

Answer

To solve the problem, let's denote the number of boys as \( n \). According to the problem, each boy contributes as many 25 paise coins as there are boys. Therefore, each boy contributes \( n \) coins of 25 paise.

1. **Calculate the total contribution of one boy**:
Each boy gives \( n \) coins of 25 paise. The total contribution from one boy can be calculated as:
\[ \text{Contribution from one boy} = n \times 25 \text{ paise} \]

2. **Calculate the total contribution from all boys**:
Since there are \( n \) boys, the total contribution from all boys can be calculated as:
\[ \text{Total contribution} = n \times (n \times 25) = 25n^2 \text{ paise} \]

3. **Convert the total amount raised to paise**:
The total amount raised is Rs. 400. To convert this into paise, we use the conversion:
\[ 1 \text{ Rs} = 100 \text{ paise} \]
Therefore,
\[ 400 \text{ Rs} = 400 \times 100 = 40000 \text{ paise} \]

4. **Set up the equation**:
Now we can set up the equation based on the total contribution:
\[ 25n^2 = 40000 \]

5. **Solve for \( n^2 \)**:
To find \( n^2 \), divide both sides of the equation by 25:
\[ n^2 = \frac{40000}{25} = 1600 \]

6. **Find \( n \)**:
Taking the square root of both sides gives:
\[ n = \sqrt{1600} = 40 \]

Thus, the number of boys is \( n = 40 \).

### Summary of Steps:
1. Define the number of boys as \( n \).
2. Calculate the contribution from one boy.
3. Calculate the total contribution from all boys.
4. Convert the total amount raised into paise.
5. Set up the equation based on the total contribution.
6. Solve for \( n \).