Luke, Caden and Vaidev had some beads in the ratio of 2 : 3 : 5. Vaidev gave 40% of his beads to Luke and Caden. As a result, Luke had the same number of beads as Caden and Vaidev had 15 fewer beads than Luke.
- What was the percentage increase in Luke's beads after receiving from Vaidev?
- How many beads did Caden have at first?
| Luke |
Caden |
Vaidev |
Total |
| 2 u |
3 u |
5 u |
10 u |
| + 2 u |
- 2 u |
|
| 3.5 u |
3.5 u |
3 u |
10 u |
(a)
Number of beads that Vaidev gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of beads that Luke and Caden each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of beads that Luke had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Luke's beads after receiving from Vaidev
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 15
3.5 u - 3 u = 15
0.5 u = 15
1 u = 15 ÷ 0.5 = 30
Number of beads that Caden had at first
= 3 u
= 3 x 30
= 90
Answer(s): (a) 75%; (b) 90
