Charlie, Luis and Tom had some pens in the ratio of 4 : 5 : 9. Tom gave 40% of his pens to Charlie and Luis. As a result, Charlie had the same number of pens as Luis and Tom had 18 fewer pens than Charlie.

1. What was the percentage increase in Charlie's pens after receiving from Tom?
2. How many pens did Luis have at first?

Charlie	Luis	Tom	Total
4 u	5 u	9 u	18 u
+ 3.6 u		- 3.6 u
6.3 u	6.3 u	5.4 u	18 u

(a)
Number of pens that Tom gave away
= 40% x 9
= ⁴⁰₁₀₀ x 9
= 3.6 u

Number of pens that Charlie and Luis each had in the end
= (18 u - 5.4 u) ÷ 2
= 12.6 u ÷ 2
= 6.3 u

Increase in the number of pens that Charlie had
= 6.3 u - 4 u
= 2.3 u

Percentage increase in Charlie's pens after receiving from Tom
= ^2.3₄ x 100%
= 57.5%

(b)
6.3 u = 5.4 u + 18
6.3 u - 5.4 u = 18
0.9 u = 18

1 u = 18 ÷ 0.9 = 20

Number of pens that Luis had at first
= 5 u
= 5 x 20
= 100

Answer(s): (a) 57.5%; (b) 100