Question

When 40% of the girls left the school assembly, the ratio of the number of boys to girls became 3 to 4. If there were w girls when the assembly started, what was the total number of boys and girls when the assembly started?

Answer 1

Number of girls at the time of the assembly started = w

Number of girls left = 40% of w

`=(40)/(100)w`

`=(2)/(5)w`

Remaining girls =
`w-(2)/(5)w`

`=(3)/(5)w`

Now, the ratio of the number of boys to girls became 3 to 4.

Let n be the number of boys.

Then,
`n:(3)/(5) w=3:4`

Or,
`(n)/(3w/5)= (3)/(4)`

`(5n)/(3w)= (3)/(4)`

20n = 9w

or, n =
`(9)/(20) w`

Total number of boys and girls =
`(9)/(20)w+ (3)/(5) w`

`= (9)/(20)w+ (12)/(20) w`

`= = (21)/(20)w`

Hence, the total number of boys and girs is
`(21)/(20) w.`