Glen, Fabian and Gabriel had some cards in the ratio of 2 : 3 : 5. Gabriel gave 40% of his cards to Glen and Fabian. As a result, Glen had the same number of cards as Fabian and Gabriel had 43 fewer cards than Glen.

1. What was the percentage increase in Glen's cards after receiving from Gabriel?
2. How many cards did Fabian have at first?

Glen	Fabian	Gabriel	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 cards that Gabriel gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of cards that Glen and Fabian each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u

Increase in the number of cards that Glen had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Glen's cards after receiving from Gabriel
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 43
3.5 u - 3 u = 43
0.5 u = 43

1 u = 43 ÷ 0.5 = 86

Number of cards that Fabian had at first
= 3 u
= 3 x 86
= 258

Answer(s): (a) 75%; (b) 258