A fruit seller sells only grapefruits and lemons. The ratio of grapefruits to lemons is 3 : 4. A total of 72 fruits are added. The number of grapefruits becomes 3 times as many as before and the number of lemons becomes 4 times as many as before. How many fruits are there at first?

	Comparing grapefruits at first and in the end	Grapefruits	Lemons	Comparing lemons at first and in the end
Before	1x3 = 3 u	3 u	4 u	1x4 = 4 u
Change		+ 72
After	3x3 = 9 u	9 u	16 u	4x4 = 16 u

The number of lemons at first is repeated.  Make the number of lemons at first the same.  LCM of 1 and 4 is 4.

The number of grapefruits at first is repeated. Make the number of grapefruits at first the same. LCM of 1 and 3 is 3.

Number of fruits at first
= 3 u + 4 u
= 7 u

Number of fruits in the end
= 9 u + 16 u
= 25 u

Number of fruits added
= 25 u - 7 u 
= 18 u

18 u = 72

1 u = 72 ÷ 18 = 4

Number of fruits at first
= 7 u
= 7 x 4
= 28

Answer(s): 28