Harry had to collect some fruits from two supermarkets and deliver some fruits to another supermarket. He collected from Supermarket Q and the ratio of oranges to lemons was 1 : 3. When he reached Supermarket R, he unloaded ¹¹₁₂ of the lemons and some oranges from his vehicle. The ratio of oranges to lemons became 3 : 4. At Supermarket S, 33 oranges and 16 lemons were collected and the number of oranges to lemons became the same.

1. How many fruits were there on his vehicle after visiting Supermarket S?
2. How many oranges were delivered to Supermarket R?

	Location	Oranges	Lemons
Comparing oranges and lemons at first	Supermarket Q	1x16 = 16 u	3x16 = 48 u
Before 1	Supermarket Q	16 u	12x4 = 48 u
Change 1	Supermarket R	- ?	- 11x4 = - 44 u
After 1	Supermarket S	3 u	1x4 = 4 u
Before 2	Supermarket S	3x1 = 3 u	4x1 = 4 u
Change 2	Supermarket S	+ 33	+ 16
After 2	Supermarket S	3 u + 33	4 u + 16

(a)
The number of lemons after unloading at Supermarket R is repeated.  Make the number of lemons left after unloading at Supermarket R the same.  LCM of 4 and 1 is 4.

The number of lemons collected at Supermarket Q is repeated.  Make the number of lemons collected at Supermarket Q the same by multiplying 3 by 16. 
 
The number of oranges and lemons in the end is the same.

4 u + 16 = 3 u + 33
4 u - 3 u = 33 - 16

1 u = 17

Number of oranges on his vehicle after collecting from Supermarket S
= 3 u + 33
= 3 x 17 + 33
= 51 + 33
= 84

Number of fruits on his vehicle after collecting from Supermarket S
= 2 x 84 
= 168 

(b)
Number of oranges delivered to Supermarket R
= 16 u - 3 u
= 13 u
= 13 x 17
= 221

Answer(s): (a) 168; (b) 221