Oliver bought some dragonfruits and grapefruits in the ratio of 2 : 3 . After buying another 12 fruits each, the ratio becomes 7 : 9. Find the number of dragonfruits and grapefruits he had at first.
| |
Dragonfruits |
Grapefruits |
Difference |
| Before |
2x2 =
4 u |
3x2 =
6 u |
1x2 =
2 u |
| Change |
+ 12 |
+ 12 |
|
| After |
7x1 =
7 u |
9x1 =
9 u |
2x1 =
2 u |
Since the same number of fruits bought for each type of fruits is the same, the difference in the number of dragonfruits and grapefruits at first and in the end remains unchanged.
Make the difference in the number of dragonfruits and grapefruits the same. LCM of 1 and 2 is 2.
Increase in the number of dragonfruits
= 7 u - 4 u
= 3 u
3 u = 12
1 u = 12 ÷ 3 = 4
Number of grapefruits and dragonfruits that Oliver had at first
= 4 u + 6 u
= 10 u
= 10 x 4
= 40
Answer(s): 40
