There were some oranges and mangosteens in Box J and Box K. In Box J, the ratio of the oranges to the number of mangosteens was 4 : 1. In Box K, the ratio of the number of oranges to the number of mangosteens was 3 : 2. There were 3 times as many fruits in Box J as in Box K. After another 40 mangosteens were put into Box K, the ratio of the number of oranges to the number of mangosteens in Box K became 1 : 4. How many fruits were there in Box J?

Box J		Box K
3x5 = 15 u		1x5 = 5 u
Oranges	Mangosteens	Oranges	Mangosteens
4x3	1x3	3	2
12 u	3 u	3 u	2 u

The total number of fruits in Box J is repeated.  Make the total number of fruits in Box J the same.  LCM of 3 and 5 is 15.

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

	Box J		Box K
	Oranges	Mangosteens	Oranges	Mangosteens
Before	12 u	3 u	3 u	2 u
Change				+ 40
After	12 u	3 u	1x3 = 3 u	4x3 = 12 u

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

Number of mangosteens put into Box K
= 12 u - 2 u
= 10 u

10 u = 40

1 u = 40 ÷ 10 = 4

Number of fruits in Box J
= 12 u + 3 u
= 15 u
= 15 x 4
= 60

Answer(s): 60