David had to collect some fruits from two markets and deliver some fruits to another market. He collected from Market B and the ratio of lemons to apples was 1 : 2. When he reached Market C, he unloaded ⁹₁₀ of the apples and some lemons from his vehicle. The ratio of lemons to apples became 2 : 3. At Market D, 31 lemons and 16 apples were collected and the number of lemons to apples became the same.

1. How many fruits were there on his vehicle after visiting Market D?
2. How many lemons were delivered to Market C?

	Location	Lemons	Apples
Comparing lemons and apples at first	Market B	1x15 = 15 u	2x15 = 30 u
Before 1	Market B	15 u	10x3 = 30 u
Change 1	Market C	- ?	- 9x3 = - 27 u
After 1	Market D	2 u	1x3 = 3 u
Before 2	Market D	2x1 = 2 u	3x1 = 3 u
Change 2	Market D	+ 31	+ 16
After 2	Market D	2 u + 31	3 u + 16

(a)
The number of apples after unloading at Market C is repeated.  Make the number of apples left after unloading at Market C the same.  LCM of 3 and 1 is 3.

The number of apples collected at Market B is repeated.  Make the number of apples collected at Market B the same by multiplying 2 by 15. 
 
The number of lemons and apples in the end is the same.

3 u + 16 = 2 u + 31
3 u - 2 u = 31 - 16

1 u = 15

Number of lemons on his vehicle after collecting from Market D
= 2 u + 31
= 2 x 15 + 31
= 30 + 31
= 61

Number of fruits on his vehicle after collecting from Market D
= 2 x 61 
= 122 

(b)
Number of lemons delivered to Market C
= 15 u - 2 u
= 13 u
= 13 x 15
= 195

Answer(s): (a) 122; (b) 195