There were some apples and persimmons in Box P and Box Q. In Box P, the ratio of the apples to the number of persimmons was 7 : 1. In Box Q, the ratio of the number of apples to the number of persimmons was 5 : 3. There were 3 times as many fruits in Box P as in Box Q. After another 42 persimmons were put into Box Q, the ratio of the number of apples to the number of persimmons in Box Q became 1 : 2. How many fruits were there in Box Q in the end?

Box P		Box Q
3x8 = 24 u		1x8 = 8 u
Apples	Persimmons	Apples	Persimmons
7x3	1x3	5	3
21 u	3 u	5 u	3 u

The total number of fruits in Box P is repeated.  Make the total number of fruits in Box P the same.  LCM of 3 and 8 is 24.

The total number of fruits in Box Q at first is repeated.  Make the total number of fruits in Box Q the same.  LCM of 1 and 8 is 8.

	Box P		Box Q
	Apples	Persimmons	Apples	Persimmons
Before	21 u	3 u	5 u	3 u
Change				+ 42
After	21 u	3 u	1x5 = 5 u	2x5 = 10 u

Number of apples in Box Q remains unchanged.  Make the number of apples in Box Q the same.  LCM of 5 and 1 is 5.

Number of persimmons put into Box Q
= 10 u - 3 u
= 7 u

7 u = 42

1 u = 42 ÷ 7 = 6

Number of fruits in Box Q in the end
= 5 u + 10 u
= 15 u
= 15 x 6
= 90

Answer(s): 90