Nick, John and Jack had some marbles in the ratio of 2 : 3 : 5. Jack gave 50% of his marbles to Nick and John. As a result, Nick had the same number of marbles as John and Jack had 40 fewer marbles than Nick.

1. What was the percentage increase in Nick's marbles after receiving from Jack?
2. How many marbles did John have at first?

Nick	John	Jack	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 marbles that Jack gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of marbles that Nick and John each had in the end
= (10 u - 2.5 u) ÷ 2
= 7.5 u ÷ 2
= 3.75 u

Increase in the number of marbles that Nick had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in Nick's marbles after receiving from Jack
= ^1.75₂ x 100%
= 87.5%

(b)
3.75 u = 2.5 u + 40
3.75 u - 2.5 u = 40
1.25 u = 40

1 u = 40 ÷ 1.25 = 32

Number of marbles that John had at first
= 3 u
= 3 x 32
= 96

Answer(s): (a) 87.5%; (b) 96