Flynn had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop S and the ratio of pomegranates to apples was 3 : 5. When he reached Shop T, he unloaded ⁹₁₀ of the apples and some pomegranates from his lorry. The ratio of pomegranates to apples became 1 : 2. At Shop U, 45 pomegranates and 32 apples were collected and the number of pomegranates to apples became the same.

1. How many fruits were there on his lorry after visiting Shop U?
2. How many pomegranates were delivered to Shop T?

	Location	Pomegranates	Apples
Comparing pomegranates and apples at first	Shop S	3x4 = 12 u	5x4 = 20 u
Before 1	Shop S	12 u	10x2 = 20 u
Change 1	Shop T	- ?	- 9x2 = - 18 u
After 1	Shop U	1 u	1x2 = 2 u
Before 2	Shop U	1x1 = 1 u	2x1 = 2 u
Change 2	Shop U	+ 45	+ 32
After 2	Shop U	1 u + 45	2 u + 32

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

The number of apples collected at Shop S is repeated.  Make the number of apples collected at Shop S the same by multiplying 5 by 4. 
 
The number of pomegranates and apples in the end is the same.

2 u + 32 = 1 u + 45
2 u - 1 u = 45 - 32

1 u = 13

Number of pomegranates on his lorry after collecting from Shop U
= 1 u + 45
= 1 x 13 + 45
= 13 + 45
= 58

Number of fruits on his lorry after collecting from Shop U
= 2 x 58 
= 116 

(b)
Number of pomegranates delivered to Shop T
= 12 u - 1 u
= 11 u
= 11 x 13
= 143

Answer(s): (a) 116; (b) 143