Perry bought some grapefruits and lemons in the ratio of 1 : 3 . After buying another 15 fruits each, the ratio becomes 5 : 12. Find the number of grapefruits and lemons he had at first.
| |
Grapefruits |
Lemons |
Difference |
| Before |
1x7 =
7 u |
3x7 =
21 u |
2x7 =
14 u |
| Change |
+ 15 |
+ 15 |
|
| After |
5x2 =
10 u |
12x2 =
24 u |
7x2 =
14 u |
Since the same number of fruits bought for each type of fruits is the same, the difference in the number of grapefruits and lemons at first and in the end remains unchanged.
Make the difference in the number of grapefruits and lemons the same. LCM of 2 and 7 is 14.
Increase in the number of grapefruits
= 10 u - 7 u
= 3 u
3 u = 15
1 u = 15 ÷ 3 = 5
Number of lemons and grapefruits that Perry had at first
= 7 u + 21 u
= 28 u
= 28 x 5
= 140
Answer(s): 140
