Each member of a picnic party contributed twice as many rupees as the total number of members and the total collection was Rs. 3042. The number of members present in the party was

Options

A. 2
B. 32
C. 40
D. 39

Answer

To solve the problem step by step, we can follow these instructions:

1. **Understand the Problem**: Each member of the picnic party contributes twice as many rupees as the total number of members, and the total collection is Rs. 3042. We need to find the number of members in the party.

2. **Define Variables**: Let the number of members in the picnic party be \( x \).

3. **Contribution Calculation**: According to the problem, each member contributes \( 2x \) rupees. Therefore, the total contribution from all members can be expressed as:
\[ \text{Total Contribution} = \text{Number of Members} \times \text{Contribution per Member} = x \times 2x = 2x^2 \]

4. **Set Up the Equation**: We know that the total contribution equals Rs. 3042. Therefore, we can set up the equation:
\[ 2x^2 = 3042 \]

5. **Solve for \( x^2 \)**: To isolate \( x^2 \), divide both sides of the equation by 2:
\[ x^2 = \frac{3042}{2} = 1521 \]

6. **Find \( x \)**: Now, take the square root of both sides to find \( x \):
\[ x = \sqrt{1521} \]

7. **Calculate the Square Root**: The square root of 1521 is 39 (since \( 39 \times 39 = 1521 \)):
\[ x = 39 \]

8. **Conclusion**: The number of members present in the party is 39.