Question

Some students planned a picnic. The total budget for food was ₹ 2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by ₹ 20. How many students attended the picnic and how much did each student pay for the food?

Answer 1

Let x be the number of students who planned a picnic. 

∴ Original cost of food for each member = ₹ `2000/x` 

Five students failed to attend the picnic. So (x – 5) students attended the picnic. 

∴ New cost of food for each member = ₹ `2000/((x - 5))` 

According to the given condition, 

₹ `2000/(x - 5)` – ₹ `2000/x` = ₹ 20 

⇒ `(2000x - 2000x + 10000)/(x(x - 5)) = 20` 

⇒ `10000/(x^2 - 5x) = 20` 

⇒ x² – 5x = 500 

⇒ x² – 5x – 500 = 0 

⇒ x² – 25x + 20x – 500 = 0 

⇒ x(x – 25) + 20(x – 25) = 0 

⇒ (x – 25)(x + 20) = 0 

⇒ x – 25 = 0 or x + 20 = 0 

⇒ x = 25 or x = –20 

∴ x = 25   ...(Number of students cannot be negative) 

Number of students who attended the picnic = x – 5

= 23 – 5

= 20 

Amount paid by each student for the food = ₹ `2000/((25 - 5))`

= ₹ `2000/20`

= ₹ 100