George, Liam and Asher had some cards in the ratio of 2 : 3 : 5. Asher gave 50% of his cards to George and Liam. As a result, George had the same number of cards as Liam and Asher had 40 fewer cards than George.

1. What was the percentage increase in George's cards after receiving from Asher?
2. How many cards did Liam have at first?

George	Liam	Asher	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 cards that Asher gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of cards that George and Liam each had in the end
= (10 u - 2.5 u) ÷ 2
= 7.5 u ÷ 2
= 3.75 u

Increase in the number of cards that George had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in George's cards after receiving from Asher
= ^1.75₂ x 100%
= 87.5%

(b)
3.75 u = 2.5 u + 40
3.75 u - 2.5 u = 40
1.25 u = 40

1 u = 40 ÷ 1.25 = 32

Number of cards that Liam had at first
= 3 u
= 3 x 32
= 96

Answer(s): (a) 87.5%; (b) 96