Ethan had to collect some fruits from two marts and deliver some fruits to another mart. He collected from Mart H and the ratio of kiwis to persimmons was 3 : 4. When he reached Mart J, he unloaded ¹¹₁₂ of the persimmons and some kiwis from his vehicle. The ratio of kiwis to persimmons became 1 : 2. At Mart K, 37 kiwis and 24 persimmons were collected and the number of kiwis to persimmons became the same.

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

	Location	Kiwis	Persimmons
Comparing kiwis and persimmons at first	Mart H	3x6 = 18 u	4x6 = 24 u
Before 1	Mart H	18 u	12x2 = 24 u
Change 1	Mart J	- ?	- 11x2 = - 22 u
After 1	Mart K	1 u	1x2 = 2 u
Before 2	Mart K	1x1 = 1 u	2x1 = 2 u
Change 2	Mart K	+ 37	+ 24
After 2	Mart K	1 u + 37	2 u + 24

(a)
The number of persimmons after unloading at Mart J is repeated.  Make the number of persimmons left after unloading at Mart J the same.  LCM of 2 and 1 is 2.

The number of persimmons collected at Mart H is repeated.  Make the number of persimmons collected at Mart H the same by multiplying 4 by 6. 
 
The number of kiwis and persimmons in the end is the same.

2 u + 24 = 1 u + 37
2 u - 1 u = 37 - 24

1 u = 13

Number of kiwis on his vehicle after collecting from Mart K
= 1 u + 37
= 1 x 13 + 37
= 13 + 37
= 50

Number of fruits on his vehicle after collecting from Mart K
= 2 x 50 
= 100 

(b)
Number of kiwis delivered to Mart J
= 18 u - 1 u
= 17 u
= 17 x 13
= 221

Answer(s): (a) 100; (b) 221