Question

Some people decided to go to a movie and spend Rs. 192 on the snacks. While going for a movie, they found that 4 people had not shown up. Therefore, the amount to be spent on snacks was recalculated, and an extra burden of Rs. 8 per person was imposed on the friends present. How many friends had planned to go to the movie initially?

• A. \(12 \)
• B. \(4 \)
• C. \(16 \)
• D. \(10 \)

Hint:

To save time, use the options. If \(x = 12\), cost = \(192/12 = 16\). If 4 don't show, people = 8, cost = \(192/8 = 24\). The difference is \(24 - 16 = 8\), which matches the question!

Answer 1

The Correct Option is A

Concept: This problem is based on the relationship between total cost, the number of people, and the cost per head.

• Total Budget: The total amount remains fixed at Rs. 192.

• Variable: Let the initial number of friends be \(x\).

Step 1: Formulating the initial and final head-costs.
Initial cost per person = \( \frac{192}{x} \) Actual number of people present = \( x - 4 \) New cost per person = \( \frac{192}{x - 4} \)

Step 2: Solving the equation based on the given burden.
The difference in cost is given as Rs. 8. \( \frac{192}{x - 4} - \frac{192}{x} = 8 \) Dividing the entire equation by 8, we get: \( \frac{24}{x - 4} - \frac{24}{x} = 1 \implies \frac{24x - 24(x - 4)}{x(x - 4)} = 1 \) \( 96 = x^2 - 4x \implies x^2 - 4x - 96 = 0 \) Factoring the quadratic: \( (x - 12)(x + 8) = 0 \). Since number of people cannot be negative,

\( x = 12 \).