Peter, Tom and Vaidev had some cards in the ratio of 5 : 6 : 11. Vaidev gave 40% of his cards to Peter and Tom. As a result, Peter had the same number of cards as Tom and Vaidev had 33 fewer cards than Peter.

1. What was the percentage increase in Peter's cards after receiving from Vaidev?
2. How many cards did Tom have at first?

Peter	Tom	Vaidev	Total
5 u	6 u	11 u	22 u
+ 4.4 u		- 4.4 u
7.7 u	7.7 u	6.6 u	22 u

(a)
Number of cards that Vaidev gave away
= 40% x 11
= ⁴⁰₁₀₀ x 11
= 4.4 u

Number of cards that Peter and Tom each had in the end
= (22 u - 6.6 u) ÷ 2
= 15.4 u ÷ 2
= 7.7 u

Increase in the number of cards that Peter had
= 7.7 u - 5 u
= 2.7 u

Percentage increase in Peter's cards after receiving from Vaidev
= ^2.7₅ x 100%
= 54%

(b)
7.7 u = 6.6 u + 33
7.7 u - 6.6 u = 33
1.1 u = 33

1 u = 33 ÷ 1.1 = 30

Number of cards that Tom had at first
= 6 u
= 6 x 30
= 180

Answer(s): (a) 54%; (b) 180