Ryan had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop P and the ratio of mangoes to starfruits was 1 : 3. When he reached Shop Q, he unloaded ⁵₆ of the starfruits and some mangoes from his lorry. The ratio of mangoes to starfruits became 1 : 2. At Shop R, 49 mangoes and 33 starfruits were collected and the number of mangoes to starfruits became the same.

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

	Location	Mangoes	Starfruits
Comparing mangoes and starfruits at first	Shop P	1x4 = 4 u	3x4 = 12 u
Before 1	Shop P	4 u	6x2 = 12 u
Change 1	Shop Q	- ?	- 5x2 = - 10 u
After 1	Shop R	1 u	1x2 = 2 u
Before 2	Shop R	1x1 = 1 u	2x1 = 2 u
Change 2	Shop R	+ 49	+ 33
After 2	Shop R	1 u + 49	2 u + 33

(a)
The number of starfruits after unloading at Shop Q is repeated.  Make the number of starfruits left after unloading at Shop Q the same.  LCM of 2 and 1 is 2.

The number of starfruits collected at Shop P is repeated.  Make the number of starfruits collected at Shop P the same by multiplying 3 by 4. 
 
The number of mangoes and starfruits in the end is the same.

2 u + 33 = 1 u + 49
2 u - 1 u = 49 - 33

1 u = 16

Number of mangoes on his lorry after collecting from Shop R
= 1 u + 49
= 1 x 16 + 49
= 16 + 49
= 65

Number of fruits on his lorry after collecting from Shop R
= 2 x 65 
= 130 

(b)
Number of mangoes delivered to Shop Q
= 4 u - 1 u
= 3 u
= 3 x 16
= 48

Answer(s): (a) 130; (b) 48