Question

Some students planned a picnic. The budget for the food was ₹ 2400. As 8 of them failed to join the party, the cost of the food for each member increased by ₹ 50. Find how many students went to the picnic.

Answer 1

Let the original number of students planned be $$n$$. 

Cost per student originally $$= ₹\ \frac{2400}{n}$$. 

Since 8 failed to join, number of students who went $$= (n - 8)$$. 

Cost per student now $$= ₹\ \frac{2400}{n - 8}$$. 

According to the problem: $$\frac{2400}{n - 8} - \frac{2400}{n} = 50$$ 

Dividing throughout by 50: $$\frac{48}{n - 8} - \frac{48}{n} = 1$$

$$48\left(\frac{n - (n - 8)}{n(n - 8)}\right) = 1$$ 

$$\frac{384}{n^2 - 8n} = 1$$

$$n^2 - 8n - 384 = 0$$ 

Factoring: $$(n - 24)(n + 16) = 0$$

$$n = 24 \quad \text{or} \quad n = -16$$ 

Since number of students cannot be negative, $$n = 24$$. 

Number of students who went to the picnic $$= n - 8 = 24 - 8 = 16$$.