Ivan had to collect some fruits from two supermarkets and deliver some fruits to another supermarket. He collected from Supermarket L and the ratio of mangoes to lemons was 1 : 2. When he reached Supermarket M, he unloaded ⁷₈ of the lemons and some mangoes from his lorry. The ratio of mangoes to lemons became 3 : 4. At Supermarket N, 54 mangoes and 40 lemons were collected and the number of mangoes to lemons became the same.

1. How many fruits were there on his lorry after visiting Supermarket N?
2. How many mangoes were delivered to Supermarket M?

	Location	Mangoes	Lemons
Comparing mangoes and lemons at first	Supermarket L	1x16 = 16 u	2x16 = 32 u
Before 1	Supermarket L	16 u	8x4 = 32 u
Change 1	Supermarket M	- ?	- 7x4 = - 28 u
After 1	Supermarket N	3 u	1x4 = 4 u
Before 2	Supermarket N	3x1 = 3 u	4x1 = 4 u
Change 2	Supermarket N	+ 54	+ 40
After 2	Supermarket N	3 u + 54	4 u + 40

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

The number of lemons collected at Supermarket L is repeated.  Make the number of lemons collected at Supermarket L the same by multiplying 2 by 16. 
 
The number of mangoes and lemons in the end is the same.

4 u + 40 = 3 u + 54
4 u - 3 u = 54 - 40

1 u = 14

Number of mangoes on his lorry after collecting from Supermarket N
= 3 u + 54
= 3 x 14 + 54
= 42 + 54
= 96

Number of fruits on his lorry after collecting from Supermarket N
= 2 x 96 
= 192 

(b)
Number of mangoes delivered to Supermarket M
= 16 u - 3 u
= 13 u
= 13 x 14
= 182

Answer(s): (a) 192; (b) 182