Question

A school had 400 girls last year and the number of boys was 95 more than that of the girls. This year the number of girls had increased by 1/5 of last years number and is 30 more than the number of boys. By what fraction had the number of boys been reduced?

Answer 1

1/11

Explanation:

The number of boys in school last year will be
`400+95=495`.

We are told that next year number of girls increased by 1/5. Next year number of girls in the school will be
`400+400*(1)/(5) =400+80=480`.

We are told that next year number of boys was 30 less than number of girls. So next year number of boys will be
`480-30=450`.

To find the factor at which number of boys reduced we will find the difference of number of boys between both years and divide by initial number of boys.

`(495-450)/(495) =(45)/(495)`

`(1)/(11)`

Therefore, number of boys had been reduced by 1/11.

Answer 2

Answer: The fraction by what the number of boys had been reduced=1/11

Explanation:

Step 1: To calculate the number of boys last year.

According to the question,

The number of boys last year= 400+95

The number of boys last year=495

Step 2: To calculate the number of girls this year.

According to the question,

The number of girls this year= 400 + 400*1/5

The number of girls this year= 480

Step 3: To calculate the number of boys this year.

According to the question,

The number of boys this year= 480 – 30

The number of boys this year=450

Step 4: To calculate the fraction by what the number of boys had been reduced.

The number of boys reduced= the number of boys last year - the number of boys this year

The number of boys reduced= 495 - 450 = 45

The fraction by what the number of boys had been reduced

= The number of boys reduced/the number of boys last year

Therefore,

The fraction by what the number of boys had been reduced= 45/495= 1/11