Xavier, Rael and Vaidev had some marbles in the ratio of 2 : 3 : 5. Vaidev gave 40% of his marbles to Xavier and Rael. As a result, Xavier had the same number of marbles as Rael and Vaidev had 11 fewer marbles than Xavier.

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

Xavier	Rael	Vaidev	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 Vaidev gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 11
3.5 u - 3 u = 11
0.5 u = 11

1 u = 11 ÷ 0.5 = 22

Number of marbles that Rael had at first
= 3 u
= 3 x 22
= 66

Answer(s): (a) 75%; (b) 66