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

1. What was the percentage increase in Daniel's cards after receiving from Oscar?
2. How many cards did Rael have at first?

Daniel	Rael	Oscar	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 Oscar gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

Percentage increase in Daniel's cards after receiving from Oscar
= ^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 Rael had at first
= 3 u
= 3 x 62
= 186

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