There were some passion fruits and pears in Box Y and Box Z. In Box Y, the ratio of the passion fruits to the number of pears was 4 : 1. In Box Z, the ratio of the number of passion fruits to the number of pears was 3 : 2. There were 2 times as many fruits in Box Y as in Box Z. After another 42 pears were put into Box Z, the ratio of the number of passion fruits to the number of pears in Box Z became 1 : 3. How many fruits were there in Box Z in the end?

Box Y		Box Z
2x5 = 10 u		1x5 = 5 u
Passion fruits	Pears	Passion fruits	Pears
4x2	1x2	3	2
8 u	2 u	3 u	2 u

The total number of fruits in Box Y is repeated.  Make the total number of fruits in Box Y the same.  LCM of 2 and 5 is 10.

The total number of fruits in Box Z at first is repeated.  Make the total number of fruits in Box Z the same.  LCM of 1 and 5 is 5.

	Box Y		Box Z
	Passion fruits	Pears	Passion fruits	Pears
Before	8 u	2 u	3 u	2 u
Change				+ 42
After	8 u	2 u	1x3 = 3 u	3x3 = 9 u

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

Number of pears put into Box Z
= 9 u - 2 u
= 7 u

7 u = 42

1 u = 42 ÷ 7 = 6

Number of fruits in Box Z in the end
= 3 u + 9 u
= 12 u
= 12 x 6
= 72

Answer(s): 72