Eric, Howard and Neave had some marbles in the ratio of 2 : 3 : 5. Neave gave 40% of his marbles to Eric and Howard. As a result, Eric had the same number of marbles as Howard and Neave had 31 fewer marbles than Eric.

1. What was the percentage increase in Eric's marbles after receiving from Neave?
2. How many marbles did Howard have at first?

Eric	Howard	Neave	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 marbles that Neave gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

Increase in the number of marbles that Eric had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Eric's marbles after receiving from Neave
= ^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 marbles that Howard had at first
= 3 u
= 3 x 62
= 186

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