Question

8. The population of a small village is in the following ratios:

• Adult Males: Children = 11:3
• Adult Women: Children = 5:2
The difference between the number of Adult Males and Adult Females is 28.
Find the number of children in the village.

Answer 1

24 children

Explanation:

Given ratios:

• Adult Males: Children = 11 : 3
• Adult Females : Children = 5 : 2

Multiply the first ratio by 2 and the second ratio by 3 so that the ratios of children are the same:

• Adult Males: Children = 11 × 2 : 3 × 2 = 22 : 6
• Adult Females : Children = 5 × 3 : 2 × 3 = 15 : 6

Therefore the combined ratio is:

• Adult Males : Adult Females : Children = 22 : 15 : 6

So the ratio of Adult Males to Adult Females is 22 : 15.

If the difference between the number of Adult Males and Adult Females is 28 then:

`\implies (22)/(22+15)x-(15)/(22+15)x=28`

`\implies (22)/(37)x-(15)/(37)x=28`

`\implies (7)/(37)x=28`

`\implies 7x=1036`

`\implies x=148`

Therefore:

`\implies \textsf{Adult Males}=(22)/(37) * 148=88`

`\implies \textsf{Adult Females}=(15)/(37) * 148=60`

If the original ratio of Adult Males to Children is 11 : 3, and the number of Adult Males is 88:

`\implies 11:3=88:c`

`\implies (11)/(3)=(88)/(c)`

`\implies 11c=264`

`\implies c=24`

Therefore, the number of children in the village is 24.