A fruit seller sells only pears and mangosteens. The ratio of pears to mangosteens is 1 : 3. A total of 30 fruits are added. The number of pears becomes 2 times as many as before and the number of mangosteens becomes 4 times as many as before. How many fruits are there at first?

	Comparing pears at first and in the end	Pears	Mangosteens	Comparing mangosteens at first and in the end
Before	1x1 = 1 u	1 u	3 u	1x3 = 3 u
Change		+ 30
After	2x1 = 2 u	2 u	12 u	4x3 = 12 u

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

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

Number of fruits at first
= 1 u + 3 u
= 4 u

Number of fruits in the end
= 2 u + 12 u
= 14 u

Number of fruits added
= 14 u - 4 u 
= 10 u

10 u = 30

1 u = 30 ÷ 10 = 3

Number of fruits at first
= 4 u
= 4 x 3
= 12

Answer(s): 12