Olivia had some mangosteens and apples in 2 boxes. In Box H, the number of mangosteens to the number of apples was in the ratio of 5 : 6. In Box J, there were four times as many mangosteens as apples. After Olivia transferred ²₃ of the apples from Box H to Box J, the number of fruits left in Box H was 175 and the ratio of the number of mangosteens to the number of apples in Box B became 3 : 7. How many fruits were in Box J in the end?

	Box H		Box J
	Mangosteens	Apples	Mangosteens	Apples
Before	5 u	6 u	4x3 =  12 p	1x3 = 3 p
Change		- 4 u		+ 4 u (+ 25 p)
After	5 u	2 u	3x4 = 12 p	7x4 = 28 p

Number of apples that Olivia transferred from Box H to Box J
= ²₃ x 6 u
= 4 u

Total number of fruits in Box H in the end
= 5 u + 2 u
= 7 u

7 u = 175
1 u = 175 ÷ 7 = 25

The number of mangosteens in Box J is the unchanged quantity.
LCM of 4 and 3 is 12.

Number of apples that Olivia transferred from Box H to Box J
= 4 u
= 4 x 25
= 100

Increase in the number of apples that due to the transfer from Box H to Box J
= 28 p - 3 p
= 25 p

25 p = 4 u 
25 p = 100

1 p = 100 ÷ 25 = 4

Number of fruits in Box J in the end
= 12 p + 28 p
= 40 p
= 40 x 4
= 160

Answer(s): 160