Three-fourth students of a class are boys. If 120 girls are added to the class, then three-fourth students of the class would be girls. What percentage increment should be there in the girls to have 40 girls in the class?
- A100%
- B133.33%
- C166.67%
- D266.67%
Solution & Step-by-step Explanation
Let the initial total number of students in the class be x.
Initial number of boys =
4
3
x
Initial number of girls =x−
4
3
x=
4
1
x
When 120 girls are added:
New number of girls =
4
1
x+120
New total number of students =x+120
According to the problem, the new number of girls is three-fourth of the new total population:
4
1
x+120=
4
3
(x+120)
4
1
x+120=
4
3
x+90
120−90=
4
3
x−
4
1
x
30=
4
2
x=
2
1
x
x=60
So, the initial number of girls =
4
1
×60=15.
The question asks for the percentage increment required on this initial number of girls to make the total number of girls exactly equal to 40.
Initial girls =15
Target girls =40
Required increment =40−15=25
Percentage increment calculation:
Percentage Increment=
Initial Girls
Required Increment
×100
Percentage Increment=
15
25
×100=
3
5
×100=166.67%
Initial number of boys =
4
3
x
Initial number of girls =x−
4
3
x=
4
1
x
When 120 girls are added:
New number of girls =
4
1
x+120
New total number of students =x+120
According to the problem, the new number of girls is three-fourth of the new total population:
4
1
x+120=
4
3
(x+120)
4
1
x+120=
4
3
x+90
120−90=
4
3
x−
4
1
x
30=
4
2
x=
2
1
x
x=60
So, the initial number of girls =
4
1
×60=15.
The question asks for the percentage increment required on this initial number of girls to make the total number of girls exactly equal to 40.
Initial girls =15
Target girls =40
Required increment =40−15=25
Percentage increment calculation:
Percentage Increment=
Initial Girls
Required Increment
×100
Percentage Increment=
15
25
×100=
3
5
×100=166.67%