Zoe had 45 as many beads as Pamela. The sum of the number of beads Zoe and Pamela had was the same as the number of beads that Usha had. After trading, Usha gave 20% of her beads to Zoe and received 20% of Pamela's beads. After that, Pamela continued to trade and increased her number of beads in the end by 20%, find the ratio of her number of beads to the sum of Zoe's and Usha's beads in the end.
| |
Zoe |
Usha |
Pamela |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
5.8 u |
8.2 u |
4 u |
|
| Change 3 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
13.2 u |
4.8 u |
18 u |
Total number of beads that Zoe and Pamela had at first
= 4 u + 5 u
= 9 u
Number of beads that Usha had at first = 9 u
Number of beads that Usha gave to Zoe
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of beads that Usha received from Pamela
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of beads that Pamela increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of beads that Zoe and Usha had in the end
= 5.8 u + 8.2 u - 0.8 u
= 13.2 u
In the end
Pamela : Zoe and Usha
4.8 : 13.2
480 : 1320
4 : 11
Answer(s): 4 : 11
