Question

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?

Answer 1

The answer is 21 : 22.

Step-by-step solution:-


Let the number of boys = 7k

and the number of girls = 8k

Due to increase in percentage,

Number of boys = 7k x 120/100 = 42k/5

Number of girls = 8k x 110/100 = 44k/5

Hence,the required ratio = (42k/5 : 44k/5) = 21:22


Alternatively,solution:-

Let the number of boys as 70 and girls as 80 .

=> Effect of rise of percentage on:-

 Boys = 20% rise = 70 + 70× 20/100 = 70 +14 = 84

Girls = 10% rise =80 + 80 × 10/100 = 80 +8 = 88

Hence,the new ratio = 84:88 = 21 : 22

Answer 2

Let the number of boys be 7x and girls be 8x.

The percentage increase in the number of boys and girls be 20% and 10% respectively.

Increased number of boys = 20% of 7x

→ 120/100×7x

→ 42x/5

Increased number of girls = 10% of 8x

→ 110/100×8x

→ 44x/5

New ratio = 42x/5 : 44x/5

→ 42x : 44x

→ 21:22