A fruit seller sells only lemons and dragonfruits. The ratio of lemons to dragonfruits is 4 : 5. A total of 110 fruits are added. The number of lemons becomes 4 times as many as before and the number of dragonfruits becomes 3 times as many as before. How many fruits are there at first?

	Comparing lemons at first and in the end	Lemons	Dragonfruits	Comparing dragonfruits at first and in the end
Before	1x4 = 4 u	4 u	5 u	1x5 = 5 u
Change		+ 110
After	4x4 = 16 u	16 u	15 u	3x5 = 15 u

The number of dragonfruits at first is repeated.  Make the number of dragonfruits at first the same.  LCM of 1 and 5 is 5.

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

Number of fruits at first
= 4 u + 5 u
= 9 u

Number of fruits in the end
= 16 u + 15 u
= 31 u

Number of fruits added
= 31 u - 9 u 
= 22 u

22 u = 110

1 u = 110 ÷ 22 = 5

Number of fruits at first
= 9 u
= 9 x 5
= 45

Answer(s): 45