The ratio of the number of boys and girls in a college is 6:7. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?
- A72 : 77
- B35 : 36
- C36 : 35
- D77 : 72
Solution & Step-by-step Explanation
Let the initial number of boys be 6x and the initial number of girls be 7x.
New number of boys after a 20% increase:
New Boys=6x×(1+
100
20
)=6x×
100
120
=6x×1.2=7.2x
New number of girls after a 10% increase:
New Girls=7x×(1+
100
10
)=7x×
100
110
=7x×1.1=7.7x
The new ratio of boys to girls is:
New Ratio=
7.7x
7.2x
=
77
72
New number of boys after a 20% increase:
New Boys=6x×(1+
100
20
)=6x×
100
120
=6x×1.2=7.2x
New number of girls after a 10% increase:
New Girls=7x×(1+
100
10
)=7x×
100
110
=7x×1.1=7.7x
The new ratio of boys to girls is:
New Ratio=
7.7x
7.2x
=
77
72