Carl bought some starfruits and pomegranates in the ratio of 1 : 3 . After buying another 54 fruits each, the ratio becomes 7 : 12. Find the number of starfruits and pomegranates he had at first.
| |
Starfruits |
Pomegranates |
Difference |
| Before |
1x5 =
5 u |
3x5 =
15 u |
2x5 =
10 u |
| Change |
+ 54 |
+ 54 |
|
| After |
7x2 =
14 u |
12x2 =
24 u |
5x2 =
10 u |
Since the same number of fruits bought for each type of fruits is the same, the difference in the number of starfruits and pomegranates at first and in the end remains unchanged.
Make the difference in the number of starfruits and pomegranates the same. LCM of 2 and 5 is 10.
Increase in the number of starfruits
= 14 u - 5 u
= 9 u
9 u = 54
1 u = 54 ÷ 9 = 6
Number of pomegranates and starfruits that Carl had at first
= 5 u + 15 u
= 20 u
= 20 x 6
= 120
Answer(s): 120
