Ryan, Xavier and Albert had some cards in the ratio of 2 : 3 : 5. Albert gave 40% of his cards to Ryan and Xavier. As a result, Ryan had the same number of cards as Xavier and Albert had 31 fewer cards than Ryan.

1. What was the percentage increase in Ryan's cards after receiving from Albert?
2. How many cards did Xavier have at first?

Ryan	Xavier	Albert	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 Albert gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 31
3.5 u - 3 u = 31
0.5 u = 31

1 u = 31 ÷ 0.5 = 62

Number of cards that Xavier had at first
= 3 u
= 3 x 62
= 186

Answer(s): (a) 75%; (b) 186