Question

Dan and Paul share some money in the ratio 9:5.

Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1.
How much did Paul originally have?

Answer 1

Paul had £40 originally.

Explanation:

Given

Let d be the money Dan has and p be the money Paul has

Then according to the given situation,

`(d)/(p) = (9)/(5)\\d = (9p)/(5)\ \ \ Equation\ 1`

Now from the statement, "Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1"

`(d-32)/(p) = 1` Eqn 2

From 2

`d - 32 = p\\`

Putting d = 9p/5

`(9p)/(5) - 32 = p\\9p - 160 = 5p\\9p-5p = 160\\4p = 160\\(4p)/(4) = (160)/(4)\\p = 40`

Checking

`d = (9(40))/(5) = (360)/(5) = 72\\(d)/(p) = (72)/(40) = (9)/(5)`

Hence,

Paul had £40 originally.