Carl, Ethan and Vincent had some coins in the ratio of 2 : 3 : 5. Vincent gave 40% of his coins to Carl and Ethan. As a result, Carl had the same number of coins as Ethan and Vincent had 45 fewer coins than Carl.

1. What was the percentage increase in Carl's coins after receiving from Vincent?
2. How many coins did Ethan have at first?

Carl	Ethan	Vincent	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 coins that Vincent gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of coins that Carl and Ethan each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u

Increase in the number of coins that Carl had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Carl's coins after receiving from Vincent
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 45
3.5 u - 3 u = 45
0.5 u = 45

1 u = 45 ÷ 0.5 = 90

Number of coins that Ethan had at first
= 3 u
= 3 x 90
= 270

Answer(s): (a) 75%; (b) 270