Cathy had some passion fruits and mangosteens in 2 baskets. In Basket E, the number of passion fruits to the number of mangosteens was in the ratio of 2 : 9. In Basket F, there were twice as many passion fruits as mangosteens. After Cathy transferred ¹₃ of the mangosteens from Basket E to Basket F, the number of fruits left in Basket E was 264 and the ratio of the number of passion fruits to the number of mangosteens in Basket B became 7 : 8. How many fruits were in Basket F in the end?

	Basket E		Basket F
	Passion Fruits	Mangosteens	Passion Fruits	Mangosteens
Before	2 u	9 u	2x7 =  14 p	1x7 = 7 p
Change		- 3 u		+ 3 u (+ 9 p)
After	2 u	6 u	7x2 = 14 p	8x2 = 16 p

Number of mangosteens that Cathy transferred from Basket E to Basket F
= ¹₃ x 9 u
= 3 u

Total number of fruits in Basket E in the end
= 2 u + 6 u
= 8 u

8 u = 264
1 u = 264 ÷ 8 = 33

The number of passion fruits in Basket F is the unchanged quantity.
LCM of 2 and 7 is 14.

Number of mangosteens that Cathy transferred from Basket E to Basket F
= 3 u
= 3 x 33
= 99

Increase in the number of mangosteens that due to the transfer from Basket E to Basket F
= 16 p - 7 p
= 9 p

9 p = 3 u 
9 p = 99

1 p = 99 ÷ 9 = 11

Number of fruits in Basket F in the end
= 14 p + 16 p
= 30 p
= 30 x 11
= 330

Answer(s): 330