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

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

Tom	Japheth	Ethan	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 Ethan gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of cards that Tom and Japheth 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 Tom had
= 3.75 u - 2 u
= 1.75 u

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

(b)
3.75 u = 2.5 u + 50
3.75 u - 2.5 u = 50
1.25 u = 50

1 u = 50 ÷ 1.25 = 40

Number of cards that Japheth had at first
= 3 u
= 3 x 40
= 120

Answer(s): (a) 87.5%; (b) 120