Usha bought a total of 80 big and small candy canes. Then she decided to exchange 50% of her big candy canes for the small ones in the ratio of 1 : 5. After the exchange, she had 112 candy canes. What percentage of the candy canes she bought were small ones?
|
Big candy canes |
Small candy canes |
Total |
Before |
2 u |
? |
80 |
Change |
- 1 u |
|
|
Comparing big and small candy canes at exchange |
- 1 u |
+ 5 u |
+ 32 |
After |
1 u |
? |
112 |
50% =
50100 =
12The number of big candy canes that were exchanged for small candy canes was repeated.
Number of extra candy canes that Usha received due to the exchange
= 5 u - 1 u
= 4 u
4 u = 112 - 80
4 u = 32
1 u = 32 ÷ 4 = 8
Number of small candy canes at first
= 80 - 2 u
= 80 - 2 x 8
= 80 - 16
= 64
Percentage of the candy canes Usha bought that were small ones
=
6480 x 100%
= 80%
Answer(s): 80%