John, Albert and Neave had some cards in the ratio of 5 : 6 : 11. Neave gave 50% of his cards to John and Albert. As a result, John had the same number of cards as Albert and Neave had 11 fewer cards than John.

1. What was the percentage increase in John's cards after receiving from Neave?
2. How many cards did Albert have at first?

John	Albert	Neave	Total
5 u	6 u	11 u	22 u
+ 5.5 u		- 5.5 u
8.25 u	8.25 u	5.5 u	22 u

(a)
Number of cards that Neave gave away
= 50% x 11
= ⁵⁰₁₀₀ x 11
= 5.5 u

Number of cards that John and Albert each had in the end
= (22 u - 5.5 u) ÷ 2
= 16.5 u ÷ 2
= 8.25 u

Increase in the number of cards that John had
= 8.25 u - 5 u
= 3.25 u

Percentage increase in John's cards after receiving from Neave
= ^3.25₅ x 100%
= 65%

(b)
8.25 u = 5.5 u + 11
8.25 u - 5.5 u = 11
2.75 u = 11

1 u = 11 ÷ 2.75 = 4

Number of cards that Albert had at first
= 6 u
= 6 x 4
= 24

Answer(s): (a) 65%; (b) 24