There were some lemons and pomegranates in Box J and Box K. In Box J, the ratio of the lemons to the number of pomegranates was 6 : 1. In Box K, the ratio of the number of lemons to the number of pomegranates was 5 : 2. There were 2 times as many fruits in Box J as in Box K. After another 144 pomegranates were put into Box K, the ratio of the number of lemons to the number of pomegranates in Box K became 1 : 4. How many fruits were there in Box K in the end?

Box J		Box K
2x7 = 14 u		1x7 = 7 u
Lemons	Pomegranates	Lemons	Pomegranates
6x2	1x2	5	2
12 u	2 u	5 u	2 u

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

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

	Box J		Box K
	Lemons	Pomegranates	Lemons	Pomegranates
Before	12 u	2 u	5 u	2 u
Change				+ 144
After	12 u	2 u	1x5 = 5 u	4x5 = 20 u

Number of lemons in Box K remains unchanged.  Make the number of lemons in Box K the same.  LCM of 5 and 1 is 5.

Number of pomegranates put into Box K
= 20 u - 2 u
= 18 u

18 u = 144

1 u = 144 ÷ 18 = 8

Number of fruits in Box K in the end
= 5 u + 20 u
= 25 u
= 25 x 8
= 200

Answer(s): 200