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Shared-expense algebra: Determine the attending headcount from a per-person increase. Total planned spend on eatables = ₹96. Four friends did not turn up. Remaining attendees each paid ₹4 extra than originally planned. Find the number of friends who attended the picnic. Choose the correct value.

Difficulty: Medium

Correct Answer: 8

Explanation:

Let
n = original number of friends, so original share = 96/n.

After 4 drop
New number = n − 4; new share = 96/(n − 4). Increase per person = 4 ⇒ 96/(n − 4) − 96/n = 4.

Solve
96·(n − (n − 4)) / [n(n − 4)] = 4 ⇒ 96·4 / [n(n − 4)] = 4 n(n − 4) = 96 ⇒ n² − 4n − 96 = 0 ⇒ (n − 12)(n + 8) = 0 ⇒ n = 12. Attended = n − 4 = 8.

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