There were some mangosteens and apples in Box N and Box P. In Box N, the ratio of the mangosteens to the number of apples was 6 : 1. In Box P, the ratio of the number of mangosteens to the number of apples was 4 : 3. There were 2 times as many fruits in Box N as in Box P. After another 10 apples were put into Box P, the ratio of the number of mangosteens to the number of apples in Box P became 1 : 2. How many fruits were there in Box N?

Box N		Box P
2x7 = 14 u		1x7 = 7 u
Mangosteens	Apples	Mangosteens	Apples
6x2	1x2	4	3
12 u	2 u	4 u	3 u

The total number of fruits in Box N is repeated.  Make the total number of fruits in Box N the same.  LCM of 2 and 7 is 14.

The total number of fruits in Box P at first is repeated.  Make the total number of fruits in Box P the same.  LCM of 1 and 7 is 7.

	Box N		Box P
	Mangosteens	Apples	Mangosteens	Apples
Before	12 u	2 u	4 u	3 u
Change				+ 10
After	12 u	2 u	1x4 = 4 u	2x4 = 8 u

Number of mangosteens in Box P remains unchanged.  Make the number of mangosteens in Box P the same.  LCM of 4 and 1 is 4.

Number of apples put into Box P
= 8 u - 3 u
= 5 u

5 u = 10

1 u = 10 ÷ 5 = 2

Number of fruits in Box N
= 12 u + 2 u
= 14 u
= 14 x 2
= 28

Answer(s): 28