A fruit seller sells only lemons and mangoes. The ratio of lemons to mangoes is 2 : 3. A total of 54 fruits are added. The number of lemons becomes 4 times as many as before and the number of mangoes becomes 2 times as many as before. How many fruits are there at first?

	Comparing lemons at first and in the end	Lemons	Mangoes	Comparing mangoes at first and in the end
Before	1x2 = 2 u	2 u	3 u	1x3 = 3 u
Change		+ 54
After	4x2 = 8 u	8 u	6 u	2x3 = 6 u

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

The number of lemons at first is repeated. Make the number of lemons at first the same. LCM of 1 and 2 is 2.

Number of fruits at first
= 2 u + 3 u
= 5 u

Number of fruits in the end
= 8 u + 6 u
= 14 u

Number of fruits added
= 14 u - 5 u 
= 9 u

9 u = 54

1 u = 54 ÷ 9 = 6

Number of fruits at first
= 5 u
= 5 x 6
= 30

Answer(s): 30