Question

16. The ratio of number of boys to the number of girls in a school of 1430 students is
7: 6. If 26 new girls are admitted in the school, find how many new boys may be
admitted so that the ratio of number of boys to the number of girls may change
to 8: 7.​

Answer 1

Answer:

Number of students = 1430

Ratio in number of boys and girls = 7 : 6

Let number of boys = 7x and of girls = 6x

7x + 6x = 1430

⇒ 13x = 1430

⇒ x = 110

Number of boys = 7x = 7 × 110 = 770

and number of girls = 6x = 6 × 110 = 660

Now adding 26 new girls, the number of girls will be = 660 + 26 = 686

Let new boys be added = y

The number of boys = 770 + y

Now new ratio = 8 : 7

770+y686 = 87

5390 + 7y = 5488

7y = 5488 – 5390 = 98

y = 14

Number of new boys admitted = 14