There were some mangosteens and persimmons in Box B and Box C. In Box B, the ratio of the mangosteens to the number of persimmons was 3 : 1. In Box C, the ratio of the number of mangosteens to the number of persimmons was 3 : 1. There were 3 times as many fruits in Box B as in Box C. After another 64 persimmons were put into Box C, the ratio of the number of mangosteens to the number of persimmons in Box C became 1 : 3. How many fruits were there in Box C in the end?

Box B		Box C
3x4 = 12 u		1x4 = 4 u
Mangosteens	Persimmons	Mangosteens	Persimmons
3x3	1x3	3	1
9 u	3 u	3 u	1 u

The total number of fruits in Box B is repeated.  Make the total number of fruits in Box B the same.  LCM of 3 and 4 is 12.

The total number of fruits in Box C at first is repeated.  Make the total number of fruits in Box C the same.  LCM of 1 and 4 is 4.

	Box B		Box C
	Mangosteens	Persimmons	Mangosteens	Persimmons
Before	9 u	3 u	3 u	1 u
Change				+ 64
After	9 u	3 u	1x3 = 3 u	3x3 = 9 u

Number of mangosteens in Box C remains unchanged.  Make the number of mangosteens in Box C the same.  LCM of 3 and 1 is 3.

Number of persimmons put into Box C
= 9 u - 1 u
= 8 u

8 u = 64

1 u = 64 ÷ 8 = 8

Number of fruits in Box C in the end
= 3 u + 9 u
= 12 u
= 12 x 8
= 96

Answer(s): 96