Archie, Japheth and Billy had some beads in the ratio of 2 : 3 : 5. Billy gave 40% of his beads to Archie and Japheth. As a result, Archie had the same number of beads as Japheth and Billy had 39 fewer beads than Archie.

1. What was the percentage increase in Archie's beads after receiving from Billy?
2. How many beads did Japheth have at first?

Archie	Japheth	Billy	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 Billy gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 39
3.5 u - 3 u = 39
0.5 u = 39

1 u = 39 ÷ 0.5 = 78

Number of beads that Japheth had at first
= 3 u
= 3 x 78
= 234

Answer(s): (a) 75%; (b) 234