Carl had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop R and the ratio of mangoes to apples was 1 : 2. When he reached Shop S, he unloaded ³₄ of the apples and some mangoes from his van. The ratio of mangoes to apples became 2 : 3. At Shop T, 23 mangoes and 16 apples were collected and the number of mangoes to apples became the same.

1. How many fruits were there on his van after visiting Shop T?
2. How many mangoes were delivered to Shop S?

	Location	Mangoes	Apples
Comparing mangoes and apples at first	Shop R	1x6 = 6 u	2x6 = 12 u
Before 1	Shop R	6 u	4x3 = 12 u
Change 1	Shop S	- ?	- 3x3 = - 9 u
After 1	Shop T	2 u	1x3 = 3 u
Before 2	Shop T	2x1 = 2 u	3x1 = 3 u
Change 2	Shop T	+ 23	+ 16
After 2	Shop T	2 u + 23	3 u + 16

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

The number of apples collected at Shop R is repeated.  Make the number of apples collected at Shop R the same by multiplying 2 by 6. 
 
The number of mangoes and apples in the end is the same.

3 u + 16 = 2 u + 23
3 u - 2 u = 23 - 16

1 u = 7

Number of mangoes on his van after collecting from Shop T
= 2 u + 23
= 2 x 7 + 23
= 14 + 23
= 37

Number of fruits on his van after collecting from Shop T
= 2 x 37 
= 74 

(b)
Number of mangoes delivered to Shop S
= 6 u - 2 u
= 4 u
= 4 x 7
= 28

Answer(s): (a) 74; (b) 28