Some friends planned a leisure trip and decided to spend Rs. 96 on eatables. 4…

Concept: When a fixed total cost is shared equally among a group and some members drop out, each remaining member's share rises by a fixed extra amount. If the total cost is C, the original group size is x, and k members do not turn up, this relationship is captured by C/(x − k) − C/x = (extra amount per person), which reduces to a quadratic equation in x.

Application:

1. Let x be the number of friends who originally planned the trip; the total amount to be spent on eatables is Rs. 96.

2. The originally planned share per person is 96/x. Since 4 people did not turn up, the (x − 4) people who came each pay 96/(x − 4).

3. Each of them paid Rs. 4 extra, so 96/(x − 4) − 96/x = 4.

4. Simplify: 96[x − (x − 4)]/[x(x − 4)] = 4, i.e. 96 × 4 = 4x(x − 4), so x(x − 4) = 96, i.e. x2 − 4x − 96 = 0.

5. Factorise: (x − 12)(x + 8) = 0, so x = 12 (x = −8 is rejected since a group size cannot be negative).

6. The number of people who actually turned up is x − 4 = 12 − 4 = 8.

Cross-check:

With 12 friends originally planning, the share would have been 96/12 = Rs. 8 each. With only 8 turning up, the share becomes 96/8 = Rs. 12 each — exactly Rs. 4 more, confirming the value.