Vincent, Fabian and Ahmad had some cards in the ratio of 2 : 3 : 5. Ahmad gave 40% of his cards to Vincent and Fabian. As a result, Vincent had the same number of cards as Fabian and Ahmad had 25 fewer cards than Vincent.

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

Vincent	Fabian	Ahmad	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 Ahmad gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of cards that Vincent 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 Vincent had
= 3.5 u - 2 u
= 1.5 u

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

(b)
3.5 u = 3 u + 25
3.5 u - 3 u = 25
0.5 u = 25

1 u = 25 ÷ 0.5 = 50

Number of cards that Fabian had at first
= 3 u
= 3 x 50
= 150

Answer(s): (a) 75%; (b) 150