Ryan had to collect some fruits from two marts and deliver some fruits to another mart. He collected from Mart R and the ratio of mangosteens to passion fruits was 2 : 3. When he reached Mart S, he unloaded ¹¹₁₂ of the passion fruits and some mangosteens from his lorry. The ratio of mangosteens to passion fruits became 3 : 4. At Mart T, 26 mangosteens and 24 passion fruits were collected and the number of mangosteens to passion fruits became the same.

1. How many fruits were there on his lorry after visiting Mart T?
2. How many mangosteens were delivered to Mart S?

	Location	Mangosteens	Passion Fruits
Comparing mangosteens and passion fruits at first	Mart R	2x16 = 32 u	3x16 = 48 u
Before 1	Mart R	32 u	12x4 = 48 u
Change 1	Mart S	- ?	- 11x4 = - 44 u
After 1	Mart T	3 u	1x4 = 4 u
Before 2	Mart T	3x1 = 3 u	4x1 = 4 u
Change 2	Mart T	+ 26	+ 24
After 2	Mart T	3 u + 26	4 u + 24

(a)
The number of passion fruits after unloading at Mart S is repeated.  Make the number of passion fruits left after unloading at Mart S the same.  LCM of 4 and 1 is 4.

The number of passion fruits collected at Mart R is repeated.  Make the number of passion fruits collected at Mart R the same by multiplying 3 by 16. 
 
The number of mangosteens and passion fruits in the end is the same.

4 u + 24 = 3 u + 26
4 u - 3 u = 26 - 24

1 u = 2

Number of mangosteens on his lorry after collecting from Mart T
= 3 u + 26
= 3 x 2 + 26
= 6 + 26
= 32

Number of fruits on his lorry after collecting from Mart T
= 2 x 32 
= 64 

(b)
Number of mangosteens delivered to Mart S
= 32 u - 3 u
= 29 u
= 29 x 2
= 58

Answer(s): (a) 64; (b) 58