A number of boys raised Rs. 12,544 for a famine fund, each boy has given as many rupees as there were boys. The number of boys was :

Options

A. 102
B. 112
C. 122
D. 132

Answer

To solve the problem step by step, we will denote the number of boys as \( x \). According to the problem, each boy contributes an amount equal to the number of boys, which means each boy contributes \( x \) rupees. Therefore, the total amount raised can be expressed as:

\[ \text{Total Amount} = \text{Number of Boys} \times \text{Contribution per Boy} = x \times x = x^2 \]

Given that the total amount raised is Rs. 12,544, we can set up the equation:

\[ x^2 = 12,544 \]

To find the number of boys, we need to calculate the square root of 12,544:

\[ x = \sqrt{12,544} \]

Now, we will calculate \( \sqrt{12,544} \).

1. **Finding the square root:**
- We can break down 12,544 into its prime factors or use a calculator to find the square root directly.
- Alternatively, we can estimate the square root by finding two perfect squares between which 12,544 lies.

2. **Calculating the square root:**
- We can start by estimating:
- \( 100^2 = 10,000 \)
- \( 110^2 = 12,100 \)
- \( 120^2 = 14,400 \)
- Therefore, \( \sqrt{12,544} \) is between 110 and 120.
- We can check \( 112^2 \):
- \( 112 \times 112 = 12,544 \)

Thus, we find that:

\[ x = 112 \]

So, the number of boys is \( \boxed{112} \).