David, Zane and Rael had some marbles in the ratio of 2 : 3 : 5. Rael gave 40% of his marbles to David and Zane. As a result, David had the same number of marbles as Zane and Rael had 49 fewer marbles than David.

1. What was the percentage increase in David's marbles after receiving from Rael?
2. How many marbles did Zane have at first?

David	Zane	Rael	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 Rael gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 49
3.5 u - 3 u = 49
0.5 u = 49

1 u = 49 ÷ 0.5 = 98

Number of marbles that Zane had at first
= 3 u
= 3 x 98
= 294

Answer(s): (a) 75%; (b) 294