Ethan had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop T and the ratio of passion fruits to lemons was 1 : 2. When he reached Shop U, he unloaded ¹¹₁₂ of the lemons and some passion fruits from his vehicle. The ratio of passion fruits to lemons became 2 : 3. At Shop V, 29 passion fruits and 12 lemons were collected and the number of passion fruits to lemons became the same.

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

	Location	Passion Fruits	Lemons
Comparing passion fruits and lemons at first	Shop T	1x18 = 18 u	2x18 = 36 u
Before 1	Shop T	18 u	12x3 = 36 u
Change 1	Shop U	- ?	- 11x3 = - 33 u
After 1	Shop V	2 u	1x3 = 3 u
Before 2	Shop V	2x1 = 2 u	3x1 = 3 u
Change 2	Shop V	+ 29	+ 12
After 2	Shop V	2 u + 29	3 u + 12

(a)
The number of lemons after unloading at Shop U is repeated.  Make the number of lemons left after unloading at Shop U the same.  LCM of 3 and 1 is 3.

The number of lemons collected at Shop T is repeated.  Make the number of lemons collected at Shop T the same by multiplying 2 by 18. 
 
The number of passion fruits and lemons in the end is the same.

3 u + 12 = 2 u + 29
3 u - 2 u = 29 - 12

1 u = 17

Number of passion fruits on his vehicle after collecting from Shop V
= 2 u + 29
= 2 x 17 + 29
= 34 + 29
= 63

Number of fruits on his vehicle after collecting from Shop V
= 2 x 63 
= 126 

(b)
Number of passion fruits delivered to Shop U
= 18 u - 2 u
= 16 u
= 16 x 17
= 272

Answer(s): (a) 126; (b) 272