Howard had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop J and the ratio of lemons to apples was 3 : 10. When he reached Shop K, he unloaded ⁹₁₀ of the apples and some lemons from his van. The ratio of lemons to apples became 3 : 4. At Shop L, 57 lemons and 48 apples were collected and the number of lemons to apples became the same.

1. How many fruits were there on his van after visiting Shop L?
2. How many lemons were delivered to Shop K?

	Location	Lemons	Apples
Comparing lemons and apples at first	Shop J	3x4 = 12 u	10x4 = 40 u
Before 1	Shop J	12 u	10x4 = 40 u
Change 1	Shop K	- ?	- 9x4 = - 36 u
After 1	Shop L	3 u	1x4 = 4 u
Before 2	Shop L	3x1 = 3 u	4x1 = 4 u
Change 2	Shop L	+ 57	+ 48
After 2	Shop L	3 u + 57	4 u + 48

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

The number of apples collected at Shop J is repeated.  Make the number of apples collected at Shop J the same by multiplying 10 by 4. 
 
The number of lemons and apples in the end is the same.

4 u + 48 = 3 u + 57
4 u - 3 u = 57 - 48

1 u = 9

Number of lemons on his van after collecting from Shop L
= 3 u + 57
= 3 x 9 + 57
= 27 + 57
= 84

Number of fruits on his van after collecting from Shop L
= 2 x 84 
= 168 

(b)
Number of lemons delivered to Shop K
= 12 u - 3 u
= 9 u
= 9 x 9
= 81

Answer(s): (a) 168; (b) 81