Ahmad, Vaidev and Sam had some beads in the ratio of 3 : 4 : 7. Sam gave 40% of his beads to Ahmad and Vaidev. As a result, Ahmad had the same number of beads as Vaidev and Sam had 49 fewer beads than Ahmad.

1. What was the percentage increase in Ahmad's beads after receiving from Sam?
2. How many beads did Vaidev have at first?

Ahmad	Vaidev	Sam	Total
3 u	4 u	7 u	14 u
+ 2.8 u		- 2.8 u
4.9 u	4.9 u	4.2 u	14 u

(a)
Number of beads that Sam gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of beads that Ahmad and Vaidev each had in the end
= (14 u - 4.2 u) ÷ 2
= 9.8 u ÷ 2
= 4.9 u

Increase in the number of beads that Ahmad had
= 4.9 u - 3 u
= 1.9 u

Percentage increase in Ahmad's beads after receiving from Sam
= ^1.9₃ x 100%
= 63.333333333333%

(b)
4.9 u = 4.2 u + 49
4.9 u - 4.2 u = 49
0.7 u = 49

1 u = 49 ÷ 0.7 = 70

Number of beads that Vaidev had at first
= 4 u
= 4 x 70
= 280

Answer(s): (a) 63.333333333333%; (b) 280