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

1. What was the percentage increase in Japheth's erasers after receiving from Valen?
2. How many erasers did Zeph have at first?

Japheth	Zeph	Valen	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 erasers that Valen gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

Increase in the number of erasers that Japheth had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Japheth's erasers after receiving from Valen
= ^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 erasers that Zeph had at first
= 3 u
= 3 x 78
= 234

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