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 originally had £40 before Dan gave him £32 to adjust the shares, making the ratio 1:1.

Step-by-step explanation:

Let's find out how much Paul originally had before Dan changed the ratio by giving him £32. The original ratio of Dan to Paul's share was 9:5. When Dan gives Paul £32, the share becomes equal, making the ratio 1:1.

Firstly, let's consider the difference in ratio parts between Dan and Paul, which is 9 - 5 = 4 parts. These 4 parts are equivalent to the £32 that Dan gave to Paul to equalize their shares.

Now, to find the value of 1 part, we would divide £32 by 4.

1 part = £32 / 4 = £8

Since Paul's original share was 5 parts, we would multiply 5 by £8 to find Paul's original amount.

Original amount Paul had = 5 parts * £8/part = £40

Therefore, Paul originally had £40 before Dan adjusted the shares to make the ratio equal.