Ian had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop G and the ratio of passion fruits to mangoes was 2 : 3. When he reached Shop H, he unloaded ⁵₆ of the mangoes and some passion fruits from his van. The ratio of passion fruits to mangoes became 2 : 3. At Shop J, 20 passion fruits and 18 mangoes were collected and the number of passion fruits to mangoes became the same.

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

	Location	Passion Fruits	Mangoes
Comparing passion fruits and mangoes at first	Shop G	2x6 = 12 u	3x6 = 18 u
Before 1	Shop G	12 u	6x3 = 18 u
Change 1	Shop H	- ?	- 5x3 = - 15 u
After 1	Shop J	2 u	1x3 = 3 u
Before 2	Shop J	2x1 = 2 u	3x1 = 3 u
Change 2	Shop J	+ 20	+ 18
After 2	Shop J	2 u + 20	3 u + 18

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

The number of mangoes collected at Shop G is repeated.  Make the number of mangoes collected at Shop G the same by multiplying 3 by 6. 
 
The number of passion fruits and mangoes in the end is the same.

3 u + 18 = 2 u + 20
3 u - 2 u = 20 - 18

1 u = 2

Number of passion fruits on his van after collecting from Shop J
= 2 u + 20
= 2 x 2 + 20
= 4 + 20
= 24

Number of fruits on his van after collecting from Shop J
= 2 x 24 
= 48 

(b)
Number of passion fruits delivered to Shop H
= 12 u - 2 u
= 10 u
= 10 x 2
= 20

Answer(s): (a) 48; (b) 20