Question

DIRECTION for the question: Solve the following question and mark the best possible option. A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. The number of those who attended the picnic was?

• A. 8
• B. 12
• C. 16
• D. 24
• E. 32

Hint:

Use equation when equal contribution changes.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Let the initial number of friends be $x$. The original contribution per person was $96/x$.
Step 2: Detailed Explanation:
Four people didn't come, so the new number of people is $x - 4$. The new contribution is $96 / (x - 4)$. The difference between the new and old contribution is Rs. 4: $$\frac{96}{x-4} - \frac{96}{x} = 4$$
Step 3: Calculation:
Dividing by 4: $\frac{24}{x-4} - \frac{24}{x} = 1$ $\frac{24x - 24(x-4)}{x(x-4)} = 1 \implies 96 = x^2 - 4x$ $x^2 - 4x - 96 = 0 \implies (x-12)(x+8) = 0$ So, $x = 12$. The number of people who attended is $x - 4 = 12 - 4 = 8$.
Step 4: Final Answer:
The number of people who attended was 8. Thus, the correct option is (a).