Rael, Howard and Pierre had some coins in the ratio of 2 : 3 : 5. Pierre gave 40% of his coins to Rael and Howard. As a result, Rael had the same number of coins as Howard and Pierre had 10 fewer coins than Rael.

1. What was the percentage increase in Rael's coins after receiving from Pierre?
2. How many coins did Howard have at first?

Rael	Howard	Pierre	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 Pierre gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 10
3.5 u - 3 u = 10
0.5 u = 10

1 u = 10 ÷ 0.5 = 20

Number of coins that Howard had at first
= 3 u
= 3 x 20
= 60

Answer(s): (a) 75%; (b) 60