There were some kiwis and passion fruits in Box J and Box K. In Box J, the ratio of the kiwis to the number of passion fruits was 6 : 1. In Box K, the ratio of the number of kiwis to the number of passion fruits was 4 : 3. There were 3 times as many fruits in Box J as in Box K. After another 65 passion fruits were put into Box K, the ratio of the number of kiwis to the number of passion fruits in Box K became 1 : 4. How many fruits were there in Box K in the end?

Box J		Box K
3x7 = 21 u		1x7 = 7 u
Kiwis	Passion fruits	Kiwis	Passion fruits
6x3	1x3	4	3
18 u	3 u	4 u	3 u

The total number of fruits in Box J is repeated.  Make the total number of fruits in Box J the same.  LCM of 3 and 7 is 21.

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
	Kiwis	Passion fruits	Kiwis	Passion fruits
Before	18 u	3 u	4 u	3 u
Change				+ 65
After	18 u	3 u	1x4 = 4 u	4x4 = 16 u

Number of kiwis in Box K remains unchanged.  Make the number of kiwis in Box K the same.  LCM of 4 and 1 is 4.

Number of passion fruits put into Box K
= 16 u - 3 u
= 13 u

13 u = 65

1 u = 65 ÷ 13 = 5

Number of fruits in Box K in the end
= 4 u + 16 u
= 20 u
= 20 x 5
= 100

Answer(s): 100