Archie had to collect some fruits from two marts and deliver some fruits to another mart. He collected from Mart G and the ratio of pears to persimmons was 2 : 3. When he reached Mart H, he unloaded ⁹₁₀ of the persimmons and some pears from his vehicle. The ratio of pears to persimmons became 2 : 3. At Mart J, 41 pears and 36 persimmons were collected and the number of pears to persimmons became the same.

1. How many fruits were there on his vehicle after visiting Mart J?
2. How many pears were delivered to Mart H?

	Location	Pears	Persimmons
Comparing pears and persimmons at first	Mart G	2x10 = 20 u	3x10 = 30 u
Before 1	Mart G	20 u	10x3 = 30 u
Change 1	Mart H	- ?	- 9x3 = - 27 u
After 1	Mart J	2 u	1x3 = 3 u
Before 2	Mart J	2x1 = 2 u	3x1 = 3 u
Change 2	Mart J	+ 41	+ 36
After 2	Mart J	2 u + 41	3 u + 36

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

The number of persimmons collected at Mart G is repeated.  Make the number of persimmons collected at Mart G the same by multiplying 3 by 10. 
 
The number of pears and persimmons in the end is the same.

3 u + 36 = 2 u + 41
3 u - 2 u = 41 - 36

1 u = 5

Number of pears on his vehicle after collecting from Mart J
= 2 u + 41
= 2 x 5 + 41
= 10 + 41
= 51

Number of fruits on his vehicle after collecting from Mart J
= 2 x 51 
= 102 

(b)
Number of pears delivered to Mart H
= 20 u - 2 u
= 18 u
= 18 x 5
= 90

Answer(s): (a) 102; (b) 90