Riordan bought some grapefruits and mangosteens in the ratio of 2 : 3 . After buying another 6 fruits each, the ratio becomes 7 : 9. Find the number of grapefruits and mangosteens he had at first.
| |
Grapefruits |
Mangosteens |
Difference |
| Before |
2x2 =
4 u |
3x2 =
6 u |
1x2 =
2 u |
| Change |
+ 6 |
+ 6 |
|
| 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 grapefruits and mangosteens at first and in the end remains unchanged.
Make the difference in the number of grapefruits and mangosteens the same. LCM of 1 and 2 is 2.
Increase in the number of grapefruits
= 7 u - 4 u
= 3 u
3 u = 6
1 u = 6 ÷ 3 = 2
Number of mangosteens and grapefruits that Riordan had at first
= 4 u + 6 u
= 10 u
= 10 x 2
= 20
Answer(s): 20
