George bought some grapefruits and starfruits in the ratio of 1 : 4 . After buying another 46 fruits each, the ratio becomes 8 : 9. Find the number of grapefruits and starfruits he has now.
| |
Grapefruits |
Starfruits |
Difference |
| Before |
1x1 =
1 u |
4x1 =
4 u |
3x1 =
3 u |
| Change |
+ 46 |
+ 46 |
|
| 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 grapefruits and starfruits at first and in the end remains unchanged.
Make the difference in the number of grapefruits and starfruits the same. LCM of 3 and 1 is 3.
Increase in the number of grapefruits
= 24 u - 1 u
= 23 u
23 u = 46
1 u = 46 ÷ 23 = 2
Number of starfruits and grapefruits that $(Fred) has now
= 24 u + 27 u
= 51 u
= 51 x 2
= 102
Answer(s): 102
