Jack had to collect some fruits from two stalls and deliver some fruits to another stall. He collected from Stall X and the ratio of mangoes to persimmons was 2 : 3. When he reached Stall Y, he unloaded ³₄ of the persimmons and some mangoes from his lorry. The ratio of mangoes to persimmons became 2 : 3. At Stall Z, 39 mangoes and 24 persimmons were collected and the number of mangoes to persimmons became the same.

1. How many fruits were there on his lorry after visiting Stall Z?
2. How many mangoes were delivered to Stall Y?

	Location	Mangoes	Persimmons
Comparing mangoes and persimmons at first	Stall X	2x4 = 8 u	3x4 = 12 u
Before 1	Stall X	8 u	4x3 = 12 u
Change 1	Stall Y	- ?	- 3x3 = - 9 u
After 1	Stall Z	2 u	1x3 = 3 u
Before 2	Stall Z	2x1 = 2 u	3x1 = 3 u
Change 2	Stall Z	+ 39	+ 24
After 2	Stall Z	2 u + 39	3 u + 24

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

The number of persimmons collected at Stall X is repeated.  Make the number of persimmons collected at Stall X the same by multiplying 3 by 4. 
 
The number of mangoes and persimmons in the end is the same.

3 u + 24 = 2 u + 39
3 u - 2 u = 39 - 24

1 u = 15

Number of mangoes on his lorry after collecting from Stall Z
= 2 u + 39
= 2 x 15 + 39
= 30 + 39
= 69

Number of fruits on his lorry after collecting from Stall Z
= 2 x 69 
= 138 

(b)
Number of mangoes delivered to Stall Y
= 8 u - 2 u
= 6 u
= 6 x 15
= 90

Answer(s): (a) 138; (b) 90