Usha had 35 as many coins as Jane. The sum of the number of coins Usha and Jane had was the same as the number of coins that Natalie had. After trading, Natalie gave 30% of her coins to Usha and received 20% of Jane's coins. After that, Jane continued to trade and increased her number of coins in the end by 10%, find the ratio of her number of coins to the sum of Usha's and Natalie's coins in the end.
| |
Usha |
Natalie |
Jane |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 2.4 u |
- 2.4 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
5.4 u |
6.6 u |
4 u |
|
| Change 3 |
- 0.4 u |
+ 0.4 u |
|
| After 2 |
11.6 u |
4.4 u |
16 u |
Total number of coins that Usha and Jane had at first
= 3 u + 5 u
= 8 u
Number of coins that Natalie had at first = 8 u
Number of coins that Natalie gave to Usha
= 30% x 8 u
=
30100 x 3 u
= 2.4 u
Number of coins that Natalie received from Jane
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of coins that Jane increased by when she continued to trade
= 10% x 4 u
=
10100 x 4 u
= 0.4 u
Number of coins that Usha and Natalie had in the end
= 5.4 u + 6.6 u - 0.4 u
= 11.6 u
In the end
Jane : Usha and Natalie
4.4 : 11.6
440 : 1160
11 : 29
Answer(s): 11 : 29
