Harry had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop P and the ratio of passion fruits to oranges was 1 : 3. When he reached Shop Q, he unloaded ¹¹₁₂ of the oranges and some passion fruits from his vehicle. The ratio of passion fruits to oranges became 1 : 2. At Shop R, 32 passion fruits and 16 oranges were collected and the number of passion fruits to oranges became the same.

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

	Location	Passion Fruits	Oranges
Comparing passion fruits and oranges at first	Shop P	1x8 = 8 u	3x8 = 24 u
Before 1	Shop P	8 u	12x2 = 24 u
Change 1	Shop Q	- ?	- 11x2 = - 22 u
After 1	Shop R	1 u	1x2 = 2 u
Before 2	Shop R	1x1 = 1 u	2x1 = 2 u
Change 2	Shop R	+ 32	+ 16
After 2	Shop R	1 u + 32	2 u + 16

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

The number of oranges collected at Shop P is repeated.  Make the number of oranges collected at Shop P the same by multiplying 3 by 8. 
 
The number of passion fruits and oranges in the end is the same.

2 u + 16 = 1 u + 32
2 u - 1 u = 32 - 16

1 u = 16

Number of passion fruits on his vehicle after collecting from Shop R
= 1 u + 32
= 1 x 16 + 32
= 16 + 32
= 48

Number of fruits on his vehicle after collecting from Shop R
= 2 x 48 
= 96 

(b)
Number of passion fruits delivered to Shop Q
= 8 u - 1 u
= 7 u
= 7 x 16
= 112

Answer(s): (a) 96; (b) 112