Tom had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop L and the ratio of passion fruits to starfruits was 1 : 2. When he reached Shop M, he unloaded ³₄ of the starfruits and some passion fruits from his van. The ratio of passion fruits to starfruits became 3 : 4. At Shop N, 18 passion fruits and 15 starfruits were collected and the number of passion fruits to starfruits became the same.

1. How many fruits were there on his van after visiting Shop N?
2. How many passion fruits were delivered to Shop M?

	Location	Passion Fruits	Starfruits
Comparing passion fruits and starfruits at first	Shop L	1x8 = 8 u	2x8 = 16 u
Before 1	Shop L	8 u	4x4 = 16 u
Change 1	Shop M	- ?	- 3x4 = - 12 u
After 1	Shop N	3 u	1x4 = 4 u
Before 2	Shop N	3x1 = 3 u	4x1 = 4 u
Change 2	Shop N	+ 18	+ 15
After 2	Shop N	3 u + 18	4 u + 15

(a)
The number of starfruits after unloading at Shop M is repeated.  Make the number of starfruits left after unloading at Shop M the same.  LCM of 4 and 1 is 4.

The number of starfruits collected at Shop L is repeated.  Make the number of starfruits collected at Shop L the same by multiplying 2 by 8. 
 
The number of passion fruits and starfruits in the end is the same.

4 u + 15 = 3 u + 18
4 u - 3 u = 18 - 15

1 u = 3

Number of passion fruits on his van after collecting from Shop N
= 3 u + 18
= 3 x 3 + 18
= 9 + 18
= 27

Number of fruits on his van after collecting from Shop N
= 2 x 27 
= 54 

(b)
Number of passion fruits delivered to Shop M
= 8 u - 3 u
= 5 u
= 5 x 3
= 15

Answer(s): (a) 54; (b) 15