A fruit seller sells only grapefruits and passion fruits. The ratio of grapefruits to passion fruits is 1 : 3. A total of 120 fruits are added. The number of grapefruits becomes 4 times as many as before and the number of passion fruits becomes 2 times as many as before. How many fruits are there at first?

	Comparing grapefruits at first and in the end	Grapefruits	Passion Fruits	Comparing passion fruits at first and in the end
Before	1x1 = 1 u	1 u	3 u	1x3 = 3 u
Change		+ 120
After	4x1 = 4 u	4 u	6 u	2x3 = 6 u

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

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

Number of fruits at first
= 1 u + 3 u
= 4 u

Number of fruits in the end
= 4 u + 6 u
= 10 u

Number of fruits added
= 10 u - 4 u 
= 6 u

6 u = 120

1 u = 120 ÷ 6 = 20

Number of fruits at first
= 4 u
= 4 x 20
= 80

Answer(s): 80