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

Answer:

Paul's original share is £ 65

Step-by-step 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 = $\frac{11x-39}{5x+39}$

According to the question,

$\frac{11x-39}{5x+39}=\frac{1}{1}$

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,

$x=\frac{78}{6}=13$

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