There were some kiwis and passion fruits in Box P and Box Q. In Box P, the ratio of the kiwis to the number of passion fruits was 6 : 1. In Box Q, the ratio of the number of kiwis to the number of passion fruits was 4 : 3. There were 2 times as many fruits in Box P as in Box Q. After another 40 passion fruits were put into Box Q, the ratio of the number of kiwis to the number of passion fruits in Box Q became 1 : 2. How many fruits were there in Box Q in the end?

Box P		Box Q
2x7 = 14 u		1x7 = 7 u
Kiwis	Passion fruits	Kiwis	Passion fruits
6x2	1x2	4	3
12 u	2 u	4 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 2 and 7 is 14.

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 7 is 7.

	Box P		Box Q
	Kiwis	Passion fruits	Kiwis	Passion fruits
Before	12 u	2 u	4 u	3 u
Change				+ 40
After	12 u	2 u	1x4 = 4 u	2x4 = 8 u

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

Number of passion fruits put into Box Q
= 8 u - 3 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

Number of fruits in Box Q in the end
= 4 u + 8 u
= 12 u
= 12 x 8
= 96

Answer(s): 96