Question
Sun April 20, 2014 By: Karen Sara

the average age of A and B is 20 years.if C were to replace A,the average would be 19 and if C were to replace B,the average would be 21.what are the ages of A,B,C?

1)22,18,20  2)18,22,20

 

3)22.20,18  4)18,20,22

explain

Expert Reply
Sun April 20, 2014
Let x,y and z be the ages of A, B and C respectively.
 
Given that the average age of A and B is 20.
 
rightwards double arrow fraction numerator x plus y over denominator 2 end fraction equals 20 rightwards double arrow x plus y equals 40.... left parenthesis 1 right parenthesis
 
Given that the average age of B and C is 19.
 
rightwards double arrow fraction numerator y plus z over denominator 2 end fraction equals 19 rightwards double arrow y plus z equals 38.... left parenthesis 2 right parenthesis
 
Given that the average age of A and C is 21.
 
rightwards double arrow fraction numerator x plus z over denominator 2 end fraction equals 21 rightwards double arrow x plus z equals 42.... left parenthesis 3 right parenthesis
 
Substitute the value of y = 38 - z from equation (2) in equation (1), we have
 
rightwards double arrow x plus 38 minus z equals 40 rightwards double arrow x minus z equals 40 minus 38 rightwards double arrow x minus z equals 2.... left parenthesis 4 right parenthesis
 
Adding equations (3) and (4), we have
 
2 x equals 44 rightwards double arrow x equals 22 S u b s t i t u t e space t h e space v a l u e space o f space x space i n space e q u a t i o n space left parenthesis 4 right parenthesis comma space w e space h a v e x minus z equals 2 rightwards double arrow 22 minus z equals 2 rightwards double arrow z equals 22 minus 2 rightwards double arrow z equals 20 S u b s t i t u t e space t h e space v a l u e space o f space z space i n space e q u a t i o n space left parenthesis 2 right parenthesis comma space w e space h a v e y plus z equals 38 rightwards double arrow y plus 20 equals 38 rightwards double arrow y equals 38 minus 20 rightwards double arrow y equals 18
Thus, the ages of x, y and z are 22, 18, 20
 
And hence the correct option is (1).
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