Dylan had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop M and the ratio of mangosteens to apples was 1 : 2. When he reached Shop N, he unloaded ⁹₁₀ of the apples and some mangosteens from his vehicle. The ratio of mangosteens to apples became 3 : 4. At Shop P, 31 mangosteens and 25 apples were collected and the number of mangosteens to apples became the same.

1. How many fruits were there on his vehicle after visiting Shop P?
2. How many mangosteens were delivered to Shop N?

	Location	Mangosteens	Apples
Comparing mangosteens and apples at first	Shop M	1x20 = 20 u	2x20 = 40 u
Before 1	Shop M	20 u	10x4 = 40 u
Change 1	Shop N	- ?	- 9x4 = - 36 u
After 1	Shop P	3 u	1x4 = 4 u
Before 2	Shop P	3x1 = 3 u	4x1 = 4 u
Change 2	Shop P	+ 31	+ 25
After 2	Shop P	3 u + 31	4 u + 25

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

The number of apples collected at Shop M is repeated.  Make the number of apples collected at Shop M the same by multiplying 2 by 20. 
 
The number of mangosteens and apples in the end is the same.

4 u + 25 = 3 u + 31
4 u - 3 u = 31 - 25

1 u = 6

Number of mangosteens on his vehicle after collecting from Shop P
= 3 u + 31
= 3 x 6 + 31
= 18 + 31
= 49

Number of fruits on his vehicle after collecting from Shop P
= 2 x 49 
= 98 

(b)
Number of mangosteens delivered to Shop N
= 20 u - 3 u
= 17 u
= 17 x 6
= 102

Answer(s): (a) 98; (b) 102