There were some passion fruits and pomegranates in Box U and Box V. In Box U, the ratio of the passion fruits to the number of pomegranates was 3 : 1. In Box V, the ratio of the number of passion fruits to the number of pomegranates was 3 : 1. There were 3 times as many fruits in Box U as in Box V. After another 30 pomegranates were put into Box V, the ratio of the number of passion fruits to the number of pomegranates in Box V became 1 : 2. How many fruits were there in Box V in the end?

Box U		Box V
3x4 = 12 u		1x4 = 4 u
Passion fruits	Pomegranates	Passion fruits	Pomegranates
3x3	1x3	3	1
9 u	3 u	3 u	1 u

The total number of fruits in Box U is repeated.  Make the total number of fruits in Box U the same.  LCM of 3 and 4 is 12.

The total number of fruits in Box V at first is repeated.  Make the total number of fruits in Box V the same.  LCM of 1 and 4 is 4.

	Box U		Box V
	Passion fruits	Pomegranates	Passion fruits	Pomegranates
Before	9 u	3 u	3 u	1 u
Change				+ 30
After	9 u	3 u	1x3 = 3 u	2x3 = 6 u

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

Number of pomegranates put into Box V
= 6 u - 1 u
= 5 u

5 u = 30

1 u = 30 ÷ 5 = 6

Number of fruits in Box V in the end
= 3 u + 6 u
= 9 u
= 9 x 6
= 54

Answer(s): 54