Peter, Paul and Neave had some beads in the ratio of 2 : 3 : 5. Neave gave 40% of his beads to Peter and Paul. As a result, Peter had the same number of beads as Paul and Neave had 10 fewer beads than Peter.
- What was the percentage increase in Peter's beads after receiving from Neave?
- How many beads did Paul have at first?
| Peter |
Paul |
Neave |
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 Neave gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of beads that Peter and Paul each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of beads that Peter had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Peter's beads after receiving from Neave
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 10
3.5 u - 3 u = 10
0.5 u = 10
1 u = 10 ÷ 0.5 = 20
Number of beads that Paul had at first
= 3 u
= 3 x 20
= 60
Answer(s): (a) 75%; (b) 60
