Question

In a class of 60 students, each boy contributed rupees equal to the number of girls and each girl contributed rupees equal to the number of boys. If the total money then collected was Rs. 1600, how many boys are there in the class?

Answer 1

Let the number of boys in the class = x 

Then number of girls in the class = 60 – x [∵ total students = 60] 

Money contributed by the boys = x(60 – x) = 60x – x² [∵ given] 

Money contributed by the girls = (60 – x)x = 60x – x² 

∴ Money contributed by the class = 120x – 2x²

By problem 120x -2x² = 1600 

⇒ 2x² – 120x + 1600 = 0 

⇒ x² – 60x + 800 = 0 

⇒ x² – 40x – 20x + 800 = 0 

⇒ x(x – 40) – 20 (x – 40) = 0 

⇒ (x – 40) (x – 20) = 0 

⇒ x = 40 (or) 20 

∴ Boys = 40 or 20 Girls = 20 or 40.