Jack had to collect some fruits from two stalls and deliver some fruits to another stall. He collected from Stall P and the ratio of starfruits to persimmons was 1 : 3. When he reached Stall Q, he unloaded ⁵₆ of the persimmons and some starfruits from his lorry. The ratio of starfruits to persimmons became 2 : 3. At Stall R, 32 starfruits and 15 persimmons were collected and the number of starfruits to persimmons became the same.

1. How many fruits were there on his lorry after visiting Stall R?
2. How many starfruits were delivered to Stall Q?

	Location	Starfruits	Persimmons
Comparing starfruits and persimmons at first	Stall P	1x6 = 6 u	3x6 = 18 u
Before 1	Stall P	6 u	6x3 = 18 u
Change 1	Stall Q	- ?	- 5x3 = - 15 u
After 1	Stall R	2 u	1x3 = 3 u
Before 2	Stall R	2x1 = 2 u	3x1 = 3 u
Change 2	Stall R	+ 32	+ 15
After 2	Stall R	2 u + 32	3 u + 15

(a)
The number of persimmons after unloading at Stall Q is repeated.  Make the number of persimmons left after unloading at Stall Q the same.  LCM of 3 and 1 is 3.

The number of persimmons collected at Stall P is repeated.  Make the number of persimmons collected at Stall P the same by multiplying 3 by 6. 
 
The number of starfruits and persimmons in the end is the same.

3 u + 15 = 2 u + 32
3 u - 2 u = 32 - 15

1 u = 17

Number of starfruits on his lorry after collecting from Stall R
= 2 u + 32
= 2 x 17 + 32
= 34 + 32
= 66

Number of fruits on his lorry after collecting from Stall R
= 2 x 66 
= 132 

(b)
Number of starfruits delivered to Stall Q
= 6 u - 2 u
= 4 u
= 4 x 17
= 68

Answer(s): (a) 132; (b) 68