Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?

Question

Philoid · Accepted Answer

Let the number of students who planned the picnic be ‘a’.

Budget for the food was Rs. 500

Cost of food for each member = 500/a

Given, 5 of these failed to go and thus the cost of food for each member increased by Rs. 5

⇒ (a – 5)(100 + a) = 100a

⇒ 100a + a² – 500 – 5a = 100a

⇒ a² – 5a – 500 = 0

⇒ a² – 25a + 20a – 500 = 0

⇒ a(a – 25) + 20(a – 25) = 0

⇒ (a + 20)(a – 25) = 0

⇒ a = 25

Number of students who attended the picnic = 25 – 5 = 20