Owen, Will and Simon had some erasers in the ratio of 2 : 3 : 5. Simon gave 40% of his erasers to Owen and Will. As a result, Owen had the same number of erasers as Will and Simon had 22 fewer erasers than Owen.

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

Owen	Will	Simon	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 Simon gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 22
3.5 u - 3 u = 22
0.5 u = 22

1 u = 22 ÷ 0.5 = 44

Number of erasers that Will had at first
= 3 u
= 3 x 44
= 132

Answer(s): (a) 75%; (b) 132