Peter had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop T and the ratio of mangoes to oranges was 1 : 3. When he reached Shop U, he unloaded ⁵₆ of the oranges and some mangoes from his van. The ratio of mangoes to oranges became 2 : 3. At Shop V, 47 mangoes and 36 oranges were collected and the number of mangoes to oranges became the same.

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

	Location	Mangoes	Oranges
Comparing mangoes and oranges at first	Shop T	1x6 = 6 u	3x6 = 18 u
Before 1	Shop T	6 u	6x3 = 18 u
Change 1	Shop U	- ?	- 5x3 = - 15 u
After 1	Shop V	2 u	1x3 = 3 u
Before 2	Shop V	2x1 = 2 u	3x1 = 3 u
Change 2	Shop V	+ 47	+ 36
After 2	Shop V	2 u + 47	3 u + 36

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

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

3 u + 36 = 2 u + 47
3 u - 2 u = 47 - 36

1 u = 11

Number of mangoes on his van after collecting from Shop V
= 2 u + 47
= 2 x 11 + 47
= 22 + 47
= 69

Number of fruits on his van after collecting from Shop V
= 2 x 69 
= 138 

(b)
Number of mangoes delivered to Shop U
= 6 u - 2 u
= 4 u
= 4 x 11
= 44

Answer(s): (a) 138; (b) 44