Vincent, Tim and Warren had some cards in the ratio of 2 : 3 : 5. Warren gave 40% of his cards to Vincent and Tim. As a result, Vincent had the same number of cards as Tim and Warren had 30 fewer cards than Vincent.

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

Vincent	Tim	Warren	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 Warren gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of cards that Vincent and Tim 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 Warren
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 30
3.5 u - 3 u = 30
0.5 u = 30

1 u = 30 ÷ 0.5 = 60

Number of cards that Tim had at first
= 3 u
= 3 x 60
= 180

Answer(s): (a) 75%; (b) 180