Tom had to collect some fruits from two supermarkets and deliver some fruits to another supermarket. He collected from Supermarket Q and the ratio of mangoes to oranges was 1 : 2. When he reached Supermarket R, he unloaded ¹¹₁₂ of the oranges and some mangoes from his vehicle. The ratio of mangoes to oranges became 3 : 4. At Supermarket S, 47 mangoes and 34 oranges were collected and the number of mangoes to oranges became the same.

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

	Location	Mangoes	Oranges
Comparing mangoes and oranges at first	Supermarket Q	1x24 = 24 u	2x24 = 48 u
Before 1	Supermarket Q	24 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	+ 47	+ 34
After 2	Supermarket S	3 u + 47	4 u + 34

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

The number of oranges collected at Supermarket Q is repeated.  Make the number of oranges collected at Supermarket Q the same by multiplying 2 by 24. 
 
The number of mangoes and oranges in the end is the same.

4 u + 34 = 3 u + 47
4 u - 3 u = 47 - 34

1 u = 13

Number of mangoes on his vehicle after collecting from Supermarket S
= 3 u + 47
= 3 x 13 + 47
= 39 + 47
= 86

Number of fruits on his vehicle after collecting from Supermarket S
= 2 x 86 
= 172 

(b)
Number of mangoes delivered to Supermarket R
= 24 u - 3 u
= 21 u
= 21 x 13
= 273

Answer(s): (a) 172; (b) 273