David, Elijah and Japheth had some cards in the ratio of 2 : 3 : 5. Japheth gave 50% of his cards to David and Elijah. As a result, David had the same number of cards as Elijah and Japheth had 20 fewer cards than David.

1. What was the percentage increase in David's cards after receiving from Japheth?
2. How many cards did Elijah have at first?

David	Elijah	Japheth	Total
2 u	3 u	5 u	10 u
+ 2.5 u		- 2.5 u
3.75 u	3.75 u	2.5 u	10 u

(a)
Number of cards that Japheth gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of cards that David and Elijah each had in the end
= (10 u - 2.5 u) ÷ 2
= 7.5 u ÷ 2
= 3.75 u

Increase in the number of cards that David had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in David's cards after receiving from Japheth
= ^1.75₂ x 100%
= 87.5%

(b)
3.75 u = 2.5 u + 20
3.75 u - 2.5 u = 20
1.25 u = 20

1 u = 20 ÷ 1.25 = 16

Number of cards that Elijah had at first
= 3 u
= 3 x 16
= 48

Answer(s): (a) 87.5%; (b) 48