There were some passion fruits and persimmons in Box P and Box Q. In Box P, the ratio of the passion fruits to the number of persimmons was 1 : 1. In Box Q, the ratio of the number of passion fruits to the number of persimmons was 3 : 1. There were 2 times as many fruits in Box P as in Box Q. After another 45 persimmons were put into Box Q, the ratio of the number of passion fruits 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
2x4 = 8 u		1x4 = 4 u
Passion fruits	Persimmons	Passion fruits	Persimmons
1x4	1x4	3	1
4 u	4 u	3 u	1 u

The total number of fruits in Box P is repeated.  Make the total number of fruits in Box P the same.  LCM of 2 and 2 is 8.

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 4 is 4.

	Box P		Box Q
	Passion fruits	Persimmons	Passion fruits	Persimmons
Before	4 u	4 u	3 u	1 u
Change				+ 45
After	4 u	4 u	1x3 = 3 u	2x3 = 6 u

Number of passion fruits in Box Q remains unchanged.  Make the number of passion fruits in Box Q the same.  LCM of 3 and 1 is 3.

Number of persimmons put into Box Q
= 6 u - 1 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

Number of fruits in Box Q in the end
= 3 u + 6 u
= 9 u
= 9 x 9
= 81

Answer(s): 81