The students of a class donated a sum of Rs 2, 209. If each student donated as many rupees as the number of students in the class, then the number of students in the class is

Options

A. 49
B. 53
C. 47
D. 51

Answer

To solve the problem, we need to find the number of students in the class, denoted as \( n \). According to the problem, each student donated an amount equal to the number of students in the class, which means each student donated \( n \) rupees.

Given that the total amount donated by all students is Rs 2,209, we can set up the equation:

\[ \text{Total Donation} = \text{Number of Students} \times \text{Donation per Student} \]

Substituting the known values into the equation, we have:

\[ 2,209 = n \times n \]

This simplifies to:

\[ n^2 = 2,209 \]

To find \( n \), we need to take the square root of both sides:

\[ n = \sqrt{2,209} \]

Now, let's calculate the square root of 2,209.

1. We can estimate the square root by finding the perfect squares around it. The perfect square of 47 is \( 2,209 \) because \( 47 \times 47 = 2,209 \).

Thus, we find:

\[ n = 47 \]

Therefore, the number of students in the class is \( 47 \).

### Summary of Steps:
1. Set up the equation based on the total donation.
2. Simplify to find \( n^2 = 2,209 \).
3. Take the square root to find \( n \).