The ratio of number of boys to that of girls in a group becomes 2: 1when 15girls leave. But. afterwards, when 45 boys also leave, the ratio becomes 1 : 5. Originally the number of girls in the group was

(1) 20 (2)30 (3)40 (4)50

Solution:

Let the original number of boys and girls be x and y respectively.

Then

x/y-15=2/1

⇒ x = 2y – 30    ……….(i)

Again, x-45/y-15=1/5

⇒ 5x-225=y-15

⇒ 5x= y-15+225

⇒ 5(2y-30) = y+210 [From equation (i))

⇒ 10y-150=y+210

⇒ 10y-y=210+150

⇒ 9y = 360

⇒ y=360/9 = 40

Then the option is (3)