Question:medium

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?

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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!
Updated On: Jun 30, 2026
  • \(12 \)
  • \(4 \)
  • \(16 \)
  • \(10 \)
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Set up the algebraic equation.
Let the initial number of friends who planned to attend = $x$; total snacks cost = Rs. 192; initial cost per person = $\frac{192}{x}$; after 4 friends did not come, number attending = $(x-4)$ and new cost per person = $\frac{192}{x-4}$.
Step 2: Apply the extra cost condition.
Each person paid Rs. 8 more than originally: $\frac{192}{x-4} - \frac{192}{x} = 8$; simplifying: $192x - 192(x-4) = 8x(x-4)$, so $768 = 8x(x-4)$, giving $x^2 - 4x - 96 = 0$.
Step 3: Solve the quadratic and verify.
Factorising: $(x-12)(x+8) = 0$, so $x = 12$; verify: initial cost = $192/12 = 16$ per person; new cost = $192/8 = 24$ per person; difference = $8$. Correct!
\[ \boxed{12} \]
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