Mark had to collect some fruits from two stalls and deliver some fruits to another stall. He collected from Stall D and the ratio of oranges to mangosteens was 1 : 3. When he reached Stall E, he unloaded ¹¹₁₂ of the mangosteens and some oranges from his lorry. The ratio of oranges to mangosteens became 1 : 2. At Stall F, 41 oranges and 37 mangosteens were collected and the number of oranges to mangosteens became the same.

1. How many fruits were there on his lorry after visiting Stall F?
2. How many oranges were delivered to Stall E?

	Location	Oranges	Mangosteens
Comparing oranges and mangosteens at first	Stall D	1x8 = 8 u	3x8 = 24 u
Before 1	Stall D	8 u	12x2 = 24 u
Change 1	Stall E	- ?	- 11x2 = - 22 u
After 1	Stall F	1 u	1x2 = 2 u
Before 2	Stall F	1x1 = 1 u	2x1 = 2 u
Change 2	Stall F	+ 41	+ 37
After 2	Stall F	1 u + 41	2 u + 37

(a)
The number of mangosteens after unloading at Stall E is repeated.  Make the number of mangosteens left after unloading at Stall E the same.  LCM of 2 and 1 is 2.

The number of mangosteens collected at Stall D is repeated.  Make the number of mangosteens collected at Stall D the same by multiplying 3 by 8. 
 
The number of oranges and mangosteens in the end is the same.

2 u + 37 = 1 u + 41
2 u - 1 u = 41 - 37

1 u = 4

Number of oranges on his lorry after collecting from Stall F
= 1 u + 41
= 1 x 4 + 41
= 4 + 41
= 45

Number of fruits on his lorry after collecting from Stall F
= 2 x 45 
= 90 

(b)
Number of oranges delivered to Stall E
= 8 u - 1 u
= 7 u
= 7 x 4
= 28

Answer(s): (a) 90; (b) 28