There were some pears and apples in Container X and Container Y. In Container X, the ratio of the pears to the number of apples was 6 : 1. In Container Y, the ratio of the number of pears to the number of apples was 4 : 3. There were 2 times as many fruits in Container X as in Container Y. After another 78 apples were put into Container Y, the ratio of the number of pears to the number of apples in Container Y became 1 : 4. How many fruits were there in Container Y in the end?

Container X		Container Y
2x7 = 14 u		1x7 = 7 u
Pears	Apples	Pears	Apples
6x2	1x2	4	3
12 u	2 u	4 u	3 u

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

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

	Container X		Container Y
	Pears	Apples	Pears	Apples
Before	12 u	2 u	4 u	3 u
Change				+ 78
After	12 u	2 u	1x4 = 4 u	4x4 = 16 u

Number of pears in Container Y remains unchanged.  Make the number of pears in Container Y the same.  LCM of 4 and 1 is 4.

Number of apples put into Container Y
= 16 u - 3 u
= 13 u

13 u = 78

1 u = 78 ÷ 13 = 6

Number of fruits in Container Y in the end
= 4 u + 16 u
= 20 u
= 20 x 6
= 120

Answer(s): 120