Elijah had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop P and the ratio of pears to chikoos was 3 : 4. When he reached Shop Q, he unloaded ³₄ of the chikoos and some pears from his lorry. The ratio of pears to chikoos became 2 : 3. At Shop R, 51 pears and 48 chikoos were collected and the number of pears to chikoos became the same.

1. How many fruits were there on his lorry after visiting Shop R?
2. How many pears were delivered to Shop Q?

	Location	Pears	Chikoos
Comparing pears and chikoos at first	Shop P	3x3 = 9 u	4x3 = 12 u
Before 1	Shop P	9 u	4x3 = 12 u
Change 1	Shop Q	- ?	- 3x3 = - 9 u
After 1	Shop R	2 u	1x3 = 3 u
Before 2	Shop R	2x1 = 2 u	3x1 = 3 u
Change 2	Shop R	+ 51	+ 48
After 2	Shop R	2 u + 51	3 u + 48

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

The number of chikoos collected at Shop P is repeated.  Make the number of chikoos collected at Shop P the same by multiplying 4 by 3. 
 
The number of pears and chikoos in the end is the same.

3 u + 48 = 2 u + 51
3 u - 2 u = 51 - 48

1 u = 3

Number of pears on his lorry after collecting from Shop R
= 2 u + 51
= 2 x 3 + 51
= 6 + 51
= 57

Number of fruits on his lorry after collecting from Shop R
= 2 x 57 
= 114 

(b)
Number of pears delivered to Shop Q
= 9 u - 2 u
= 7 u
= 7 x 3
= 21

Answer(s): (a) 114; (b) 21