Fanny had 45 as many beads as Zara. The sum of the number of beads Fanny and Zara had was the same as the number of beads that Risa had. After trading, Risa gave 20% of her beads to Fanny and received 25% of Zara's beads. After that, Zara 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 Fanny's and Risa's beads in the end.
| |
Fanny |
Risa |
Zara |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
5.8 u |
8.45 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
13.5 u |
4.5 u |
18 u |
Total number of beads that Fanny and Zara had at first
= 4 u + 5 u
= 9 u
Number of beads that Risa had at first = 9 u
Number of beads that Risa gave to Fanny
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of beads that Risa received from Zara
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of beads that Zara increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of beads that Fanny and Risa had in the end
= 5.8 u + 8.45 u - 0.75 u
= 13.5 u
In the end
Zara : Fanny and Risa
4.5 : 13.5
450 : 1350
1 : 3
Answer(s): 1 : 3
