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 1600. How many boys were there in the class?​

Answer 1

⇒  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

∴  60x−x2+60x−x2=1600

⇒  −2x2+120x−1600=0

⇒  −2(x2−60x+800)=0

⇒  x2−60x+800=0

⇒  x2−40x−20x+800=0

⇒  x(x−40)−20(x−40)=0

⇒  (x−40)(x−20)=0

∴   x=40 and x=20

∴  Number of boys in class are 20 or 40

Hope it is helpful to you.

Answer 2

Answer:

40 girls 20boys

Step-by-step explanation:

total students =60

girls=x

boys=60-x

amount contributed by boys =(60-x)x

amount contributed by girls =x(60-×)

(60-x)x+x(60-x)=1600

60x-x²+60x-x²=1600

120x-2x²-1600=0

2(x²-60x-800)=0

x²-60x-800=0

x²-40x-20x-800=0

x(x-40)+20(x-40)=0

(x-40)(x+20)=0

x-40=0. x+20=0

x=40. x=-20

students in class won't be in negative so x=40

then 60-40=20

girls are 40

boys are 20

I hope this help to you✌✌