Justin, Vincent and Ivan had some beads in the ratio of 2 : 3 : 5. Ivan gave 40% of his beads to Justin and Vincent. As a result, Justin had the same number of beads as Vincent and Ivan had 34 fewer beads than Justin.

1. What was the percentage increase in Justin's beads after receiving from Ivan?
2. How many beads did Vincent have at first?

Justin	Vincent	Ivan	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 beads that Ivan gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of beads that Justin and Vincent each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u

Increase in the number of beads that Justin had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Justin's beads after receiving from Ivan
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 34
3.5 u - 3 u = 34
0.5 u = 34

1 u = 34 ÷ 0.5 = 68

Number of beads that Vincent had at first
= 3 u
= 3 x 68
= 204

Answer(s): (a) 75%; (b) 204