in a class, 60% of students are boys, and remaining are girls. For a charity program, each boy and each girl contributed a fixed amount. if the total collection from boys and girls is in ratio 4:5, the contribution of each boy is what percentage of contribution of each girl
Answers
Step-by-step explanation:
Case 1:
If number of boys = 40
Number of girls = (60-40)=20
Case 2:
If number of boys = 20
Number of girls = (60-20)=40
Step-by-step explanation:
Total students in the class = 60
Let number of boys = x
number of girls = 60-x
Contribution of each boy = Rs(60-x)
Contribution of each girl = Rs x
Total amount collected = 1600
=> x(60-x)+(60-x)x=1600
\implies 2x(60-x)=1600⟹2x(60−x)=1600
\implies 60x-x^{2}=\frac{1600}{2}⟹60x−x
2
=
2
1600
\implies 60x-x^{2}=800⟹60x−x
2
=800
\implies x^{2}-60x+800=0⟹x
2
−60x+800=0
\implies x^{2}-40x-20x+800=0⟹x
2
−40x−20x+800=0
\implies x(x-40)-20(x-40)=0⟹x(x−40)−20(x−40)=0
\implies (x-40)(x-20)=0⟹(x−40)(x−20)=0
\implies x-40=0\:Or \: x-20=0⟹x−40=0Orx−20=0
\implies x=40\:Or \: x=20⟹x=40Orx=20
Therefore,
Case 1:
If number of boys = 40
Number of girls = (60-40)=20
Case 2:
If number of boys = 20
Number of girls = (60-20)=40