Paul, Owen and Oscar had some erasers in the ratio of 2 : 3 : 5. Oscar gave 50% of his erasers to Paul and Owen. As a result, Paul had the same number of erasers as Owen and Oscar had 50 fewer erasers than Paul.

1. What was the percentage increase in Paul's erasers after receiving from Oscar?
2. How many erasers did Owen have at first?

Paul	Owen	Oscar	Total
2 u	3 u	5 u	10 u
+ 2.5 u		- 2.5 u
3.75 u	3.75 u	2.5 u	10 u

(a)
Number of erasers that Oscar gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of erasers that Paul and Owen each had in the end
= (10 u - 2.5 u) ÷ 2
= 7.5 u ÷ 2
= 3.75 u

Increase in the number of erasers that Paul had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in Paul's erasers after receiving from Oscar
= ^1.75₂ x 100%
= 87.5%

(b)
3.75 u = 2.5 u + 50
3.75 u - 2.5 u = 50
1.25 u = 50

1 u = 50 ÷ 1.25 = 40

Number of erasers that Owen had at first
= 3 u
= 3 x 40
= 120

Answer(s): (a) 87.5%; (b) 120