There were some pears and passion fruits in Box P and Box Q. In Box P, the ratio of the pears to the number of passion fruits was 3 : 1. In Box Q, the ratio of the number of pears to the number of passion fruits was 3 : 1. There were 3 times as many fruits in Box P as in Box Q. After another 99 passion fruits were put into Box Q, the ratio of the number of pears to the number of passion fruits in Box Q became 1 : 4. How many fruits were there in Box Q in the end?

Box P		Box Q
3x4 = 12 u		1x4 = 4 u
Pears	Passion fruits	Pears	Passion fruits
3x3	1x3	3	1
9 u	3 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 3 and 4 is 12.

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
	Pears	Passion fruits	Pears	Passion fruits
Before	9 u	3 u	3 u	1 u
Change				+ 99
After	9 u	3 u	1x3 = 3 u	4x3 = 12 u

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

Number of passion fruits put into Box Q
= 12 u - 1 u
= 11 u

11 u = 99

1 u = 99 ÷ 11 = 9

Number of fruits in Box Q in the end
= 3 u + 12 u
= 15 u
= 15 x 9
= 135

Answer(s): 135