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

Box F		Box G
2x7 = 14 u		1x7 = 7 u
Passion fruits	Pomegranates	Passion fruits	Pomegranates
6x2	1x2	4	3
12 u	2 u	4 u	3 u

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

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

	Box F		Box G
	Passion fruits	Pomegranates	Passion fruits	Pomegranates
Before	12 u	2 u	4 u	3 u
Change				+ 40
After	12 u	2 u	1x4 = 4 u	2x4 = 8 u

Number of passion fruits in Box G remains unchanged.  Make the number of passion fruits in Box G the same.  LCM of 4 and 1 is 4.

Number of pomegranates put into Box G
= 8 u - 3 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

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

Answer(s): 96