Gabriel, Simon and Paul had some beads in the ratio of 2 : 3 : 5. Paul gave 40% of his beads to Gabriel and Simon. As a result, Gabriel had the same number of beads as Simon and Paul had 50 fewer beads than Gabriel.

1. What was the percentage increase in Gabriel's beads after receiving from Paul?
2. How many beads did Simon have at first?

Gabriel	Simon	Paul	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 Paul gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 50
3.5 u - 3 u = 50
0.5 u = 50

1 u = 50 ÷ 0.5 = 100

Number of beads that Simon had at first
= 3 u
= 3 x 100
= 300

Answer(s): (a) 75%; (b) 300