Ahmad, Carl and Daniel had some erasers in the ratio of 6 : 7 : 13. Daniel gave 50% of his erasers to Ahmad and Carl. As a result, Ahmad had the same number of erasers as Carl and Daniel had 26 fewer erasers than Ahmad.

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

Ahmad	Carl	Daniel	Total
6 u	7 u	13 u	26 u
+ 6.5 u		- 6.5 u
9.75 u	9.75 u	6.5 u	26 u

(a)
Number of erasers that Daniel gave away
= 50% x 13
= ⁵⁰₁₀₀ x 13
= 6.5 u

Number of erasers that Ahmad and Carl each had in the end
= (26 u - 6.5 u) ÷ 2
= 19.5 u ÷ 2
= 9.75 u

Increase in the number of erasers that Ahmad had
= 9.75 u - 6 u
= 3.75 u

Percentage increase in Ahmad's erasers after receiving from Daniel
= ^3.75₆ x 100%
= 62.5%

(b)
9.75 u = 6.5 u + 26
9.75 u - 6.5 u = 26
3.25 u = 26

1 u = 26 ÷ 3.25 = 8

Number of erasers that Carl had at first
= 7 u
= 7 x 8
= 56

Answer(s): (a) 62.5%; (b) 56