Carl, Vaidev and Ethan had some marbles in the ratio of 4 : 5 : 9. Ethan gave 50% of his marbles to Carl and Vaidev. As a result, Carl had the same number of marbles as Vaidev and Ethan had 36 fewer marbles than Carl.

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

Carl	Vaidev	Ethan	Total
4 u	5 u	9 u	18 u
+ 4.5 u		- 4.5 u
6.75 u	6.75 u	4.5 u	18 u

(a)
Number of marbles that Ethan gave away
= 50% x 9
= ⁵⁰₁₀₀ x 9
= 4.5 u

Number of marbles that Carl and Vaidev each had in the end
= (18 u - 4.5 u) ÷ 2
= 13.5 u ÷ 2
= 6.75 u

Increase in the number of marbles that Carl had
= 6.75 u - 4 u
= 2.75 u

Percentage increase in Carl's marbles after receiving from Ethan
= ^2.75₄ x 100%
= 68.75%

(b)
6.75 u = 4.5 u + 36
6.75 u - 4.5 u = 36
2.25 u = 36

1 u = 36 ÷ 2.25 = 16

Number of marbles that Vaidev had at first
= 5 u
= 5 x 16
= 80

Answer(s): (a) 68.75%; (b) 80