Question

In a class of 60 students, each boy contributed rupees equal to the number of girls and each girl contributed rupees equal to number of boys. If total money then collected was rs1600.How many boys were there in class​

Answer 1

Given:

• Total no. of student = 60
• money contributed by boys was equal to the money contributed by Girls .
• total money collected by boys was a
• Rs. 1600

To Find :

total Number of boys in the class

Solution :

Let boys be x, then girls be 60−x

Let boys be x, then girls be 60−x⇒  Contribution by boys = x(60-x)

⇒ Contribution by girls = (60-x) x

Total money collected = Rs. 1600

$\sf \: 60x - {x}^{2} + 60x - {x}^{2} = 1600 \\ \sf - 2 {x}^{2} + 120x - 1600 = 0 \\ \sf - 2( {x}^{2} - 60x - + 800) = 0 \\ \sf x(x - 40) - 20(x - 40) = 0 \\ \sf (x - 40)(x - 20) = 0 \\ \sf \: x = 20 \: and \: 40 \\ \\ \sf{no. \: of \: boys \: in \: the \: class \: is \: either \: 20 \: or \: 40}$