A fruit seller sells only pears and grapefruits. The ratio of pears to grapefruits is 4 : 5. A total of 27 fruits are added. The number of pears becomes 2 times as many as before and the number of grapefruits becomes 2 times as many as before. How many fruits are there in the end?

	Comparing pears at first and in the end	Pears	Grapefruits	Comparing grapefruits at first and in the end
Before	1x4 = 4 u	4 u	5 u	1x5 = 5 u
Change		+ 27
After	2x4 = 8 u	8 u	10 u	2x5 = 10 u

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

The number of pears at first is repeated. Make the number of pears 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
= 8 u + 10 u
= 18 u

Number of fruits added
= 18 u - 9 u 
= 9 u

9 u = 27

1 u = 27 ÷ 9 = 3

Number of fruits in the end
= 18 u
= 18 x 3
= 54

Answer(s): 54