Question

Dan and Paul share some money in the ratio 11:5. Dan decides this is unfair so he gives Paul £39 of his share to make the ratio 1:1. How much did Paul originally have?

Answer 1

Paul's original share is £ 65

Explanation:

Given,

The ratio of money Dan and Paul has = 11 : 5

Let, Dan's share = 11x,

Paul's share = 5x,

Where,

x is any positive real numbers,

Now, if Dan gives Paul £39 of his share,

Then, Dan's share = 11x - 39,

Paul's share = 5x + 39

Thus, the new ratio of there share =
`(11x-39)/(5x+39)`

According to the question,

`(11x-39)/(5x+39)=(1)/(1)`

By cross multiplication,

`11x - 39 = 5x + 39`

By additive property of equality,

`11x = 5x + 39 + 39`

By subtraction property of equality,

`11x - 5x = 78`

`6x = 78`

By division property of equality,

`x=(78)/(6)=13`

Hence, Paul's original share = 5(13) = £ 65