The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio? Correct Answer 21 : 22

Originally, let the number of boys and girls in the college be 7x and 8x respectively
Their increased number is (120% of 7x) and (110% of 8x)
$$\eqalign{ & \Rightarrow \left( {\frac{{120}}{{100}} \times 7x} \right)\,{\text{and}}\,\left( {\frac{{110}}{{100}} \times 8x} \right) \cr & \Rightarrow \frac{{42x}}{5}\,{\text{and}}\,\frac{{44x}}{5} \cr & \therefore {\text{The}}\,{\text{required}}\,{\text{ration}} \cr & = {\frac{{42x}}{5}:\frac{{44x}}{5}} \cr & = 21:22 \cr} $$