Gabriel, Xavier and Daniel had some erasers in the ratio of 2 : 3 : 5. Daniel gave 40% of his erasers to Gabriel and Xavier. As a result, Gabriel had the same number of erasers as Xavier and Daniel had 41 fewer erasers than Gabriel.

1. What was the percentage increase in Gabriel's erasers after receiving from Daniel?
2. How many erasers did Xavier have at first?

Gabriel	Xavier	Daniel	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 Daniel gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 41
3.5 u - 3 u = 41
0.5 u = 41

1 u = 41 ÷ 0.5 = 82

Number of erasers that Xavier had at first
= 3 u
= 3 x 82
= 246

Answer(s): (a) 75%; (b) 246