Riordan bought some persimmons and starfruits in the ratio of 1 : 4 . After buying another 138 fruits each, the ratio becomes 8 : 9. Find the number of persimmons and starfruits he had at first.
|
Persimmons |
Starfruits |
Difference |
Before |
1x1 = 1 u |
4x1 = 4 u |
3x1 = 3 u |
Change |
+ 138 |
+ 138 |
|
After |
8x3 = 24 u |
9x3 = 27 u |
1x3 = 3 u |
Since the same number of fruits bought for each type of fruits is the same, the difference in the number of persimmons and starfruits at first and in the end remains unchanged.
Make the difference in the number of persimmons and starfruits the same. LCM of 3 and 1 is 3.
Increase in the number of persimmons
= 24 u - 1 u
= 23 u
23 u = 138
1 u = 138 ÷ 23 = 6
Number of starfruits and persimmons that Riordan had at first
= 1 u + 4 u
= 5 u
= 5 x 6
= 30
Answer(s): 30