Paul, Liam and Ivan had some erasers in the ratio of 2 : 3 : 5. Ivan gave 40% of his erasers to Paul and Liam. As a result, Paul had the same number of erasers as Liam and Ivan had 48 fewer erasers than Paul.

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

Paul	Liam	Ivan	Total
2 u	3 u	5 u	10 u
+ 2 u		- 2 u
3.5 u	3.5 u	3 u	10 u

(a)
Number of erasers that Ivan gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of erasers that Paul and Liam each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u

Increase in the number of erasers that Paul had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Paul's erasers after receiving from Ivan
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 48
3.5 u - 3 u = 48
0.5 u = 48

1 u = 48 ÷ 0.5 = 96

Number of erasers that Liam had at first
= 3 u
= 3 x 96
= 288

Answer(s): (a) 75%; (b) 288