There were some apples and mangosteens in Box W and Box X. In Box W, the ratio of the apples to the number of mangosteens was 4 : 1. In Box X, the ratio of the number of apples to the number of mangosteens was 3 : 2. There were 2 times as many fruits in Box W as in Box X. After another 56 mangosteens were put into Box X, the ratio of the number of apples to the number of mangosteens in Box X became 1 : 3. How many fruits were there in Box X in the end?

Box W		Box X
2x5 = 10 u		1x5 = 5 u
Apples	Mangosteens	Apples	Mangosteens
4x2	1x2	3	2
8 u	2 u	3 u	2 u

The total number of fruits in Box W is repeated.  Make the total number of fruits in Box W the same.  LCM of 2 and 5 is 10.

The total number of fruits in Box X at first is repeated.  Make the total number of fruits in Box X the same.  LCM of 1 and 5 is 5.

	Box W		Box X
	Apples	Mangosteens	Apples	Mangosteens
Before	8 u	2 u	3 u	2 u
Change				+ 56
After	8 u	2 u	1x3 = 3 u	3x3 = 9 u

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

Number of mangosteens put into Box X
= 9 u - 2 u
= 7 u

7 u = 56

1 u = 56 ÷ 7 = 8

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

Answer(s): 96