A fruit seller sells only persimmons and kiwis. The ratio of persimmons to kiwis is 2 : 5. A total of 51 fruits are added. The number of persimmons becomes 2 times as many as before and the number of kiwis becomes 4 times as many as before. How many fruits are there at first?

	Comparing persimmons at first and in the end	Persimmons	Kiwis	Comparing kiwis at first and in the end
Before	1x2 = 2 u	2 u	5 u	1x5 = 5 u
Change		+ 51
After	2x2 = 4 u	4 u	20 u	4x5 = 20 u

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

The number of persimmons at first is repeated. Make the number of persimmons 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
= 4 u + 20 u
= 24 u

Number of fruits added
= 24 u - 7 u 
= 17 u

17 u = 51

1 u = 51 ÷ 17 = 3

Number of fruits at first
= 7 u
= 7 x 3
= 21

Answer(s): 21