Daniel, Dylan and Andy had some marbles in the ratio of 2 : 3 : 5. Andy gave 40% of his marbles to Daniel and Dylan. As a result, Daniel had the same number of marbles as Dylan and Andy had 40 fewer marbles than Daniel.

1. What was the percentage increase in Daniel's marbles after receiving from Andy?
2. How many marbles did Dylan have at first?

Daniel	Dylan	Andy	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 Andy gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 40
3.5 u - 3 u = 40
0.5 u = 40

1 u = 40 ÷ 0.5 = 80

Number of marbles that Dylan had at first
= 3 u
= 3 x 80
= 240

Answer(s): (a) 75%; (b) 240