Valen, Vaidev and Luke had some stamps in the ratio of 3 : 4 : 7. Luke gave 50% of his stamps to Valen and Vaidev. As a result, Valen had the same number of stamps as Vaidev and Luke had 49 fewer stamps than Valen.

1. What was the percentage increase in Valen's stamps after receiving from Luke?
2. How many stamps did Vaidev have at first?

Valen	Vaidev	Luke	Total
3 u	4 u	7 u	14 u
+ 3.5 u		- 3.5 u
5.25 u	5.25 u	3.5 u	14 u

(a)
Number of stamps that Luke gave away
= 50% x 7
= ⁵⁰₁₀₀ x 7
= 3.5 u

Number of stamps that Valen and Vaidev each had in the end
= (14 u - 3.5 u) ÷ 2
= 10.5 u ÷ 2
= 5.25 u

Increase in the number of stamps that Valen had
= 5.25 u - 3 u
= 2.25 u

Percentage increase in Valen's stamps after receiving from Luke
= ^2.25₃ x 100%
= 75%

(b)
5.25 u = 3.5 u + 49
5.25 u - 3.5 u = 49
1.75 u = 49

1 u = 49 ÷ 1.75 = 28

Number of stamps that Vaidev had at first
= 4 u
= 4 x 28
= 112

Answer(s): (a) 75%; (b) 112