Charlie bought some peaches and grapefruits in the ratio of 1 : 5 . After buying another 26 fruits each, the ratio becomes 5 : 12. Find the number of peaches and grapefruits he had at first.
| |
Peaches |
Grapefruits |
Difference |
| Before |
1x7 =
7 u |
5x7 =
35 u |
4x7 =
28 u |
| Change |
+ 26 |
+ 26 |
|
| After |
5x4 =
20 u |
12x4 =
48 u |
7x4 =
28 u |
Since the same number of fruits bought for each type of fruits is the same, the difference in the number of peaches and grapefruits at first and in the end remains unchanged.
Make the difference in the number of peaches and grapefruits the same. LCM of 4 and 7 is 28.
Increase in the number of peaches
= 20 u - 7 u
= 13 u
13 u = 26
1 u = 26 ÷ 13 = 2
Number of grapefruits and peaches that Charlie had at first
= 7 u + 35 u
= 42 u
= 42 x 2
= 84
Answer(s): 84
