Sean, Archie and Reggie had some marbles in the ratio of 2 : 3 : 5. Reggie gave 40% of his marbles to Sean and Archie. As a result, Sean had the same number of marbles as Archie and Reggie had 36 fewer marbles than Sean.

1. What was the percentage increase in Sean's marbles after receiving from Reggie?
2. How many marbles did Archie have at first?

Sean	Archie	Reggie	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 Reggie gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

Percentage increase in Sean's marbles after receiving from Reggie
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 36
3.5 u - 3 u = 36
0.5 u = 36

1 u = 36 ÷ 0.5 = 72

Number of marbles that Archie had at first
= 3 u
= 3 x 72
= 216

Answer(s): (a) 75%; (b) 216