A fruit seller sells only mangoes and lemons. The ratio of mangoes to lemons is 2 : 5. A total of 84 fruits are added. The number of mangoes becomes 3 times as many as before and the number of lemons becomes 3 times as many as before. How many fruits are there at first?

	Comparing mangoes at first and in the end	Mangoes	Lemons	Comparing lemons at first and in the end
Before	1x2 = 2 u	2 u	5 u	1x5 = 5 u
Change		+ 84
After	3x2 = 6 u	6 u	15 u	3x5 = 15 u

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

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

Number of fruits at first
= 2 u + 5 u
= 7 u

Number of fruits in the end
= 6 u + 15 u
= 21 u

Number of fruits added
= 21 u - 7 u 
= 14 u

14 u = 84

1 u = 84 ÷ 14 = 6

Number of fruits at first
= 7 u
= 7 x 6
= 42

Answer(s): 42