Some students planned a picnic. The budget for the food was ₹ 2,400. 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.

Let the original number of students be x.

In first case:

Given,

Budget of food = ₹ 2,400

Cost per person = ₹ $\dfrac{2400}{x}$

In second case :

Given,

8 students failed to join, number of students who went = x - 8

Cost per person = ₹ $\dfrac{2400}{x - 8}$

When 8 students failed to join the party, the cost of the food for each member increased by ₹ 50.

$\therefore \dfrac{2400}{x - 8} - \dfrac{2400}{x} = 50 \\[1em] \Rightarrow \dfrac{2400x - 2400(x - 8)}{x(x - 8)} = 50 \\[1em] \Rightarrow \dfrac{2400x - 2400x + 19200}{x^2 - 8x} = 50 \\[1em] \Rightarrow 19200 = 50(x^2 - 8x) \\[1em] \Rightarrow \dfrac{19200}{50} = (x^2 - 8x) \\[1em] \Rightarrow 384 = x^2 - 8x \\[1em] \Rightarrow x^2 - 8x - 384 = 0 \\[1em] \Rightarrow x^2 - 24x + 16x - 384 = 0 \\[1em] \Rightarrow x(x - 24) + 16(x - 24) = 0 \\[1em] \Rightarrow (x + 16)(x - 24) = 0 \\[1em] \Rightarrow (x + 16) = 0 \text{ or } (x - 24) = 0 \text{….[Using zero-product rule]} \\[1em] \Rightarrow x = -16 \text{ or } x = 24$

Since, number of students cannot be negative.

Thus, x = 24.

Hence, number of students went to picnic = 24.