Question

Average age of a, b & c was 28 years 2 years ago,b & c average age 4 years ago was 21 years what is the age of a?

Answer 1

Age of a

Answer:

Age of a is 40 years

Explanation:

lets assume present age of a = x

And assume present age of b = y

And assume present age of c = z

TWO YEARS AGO

age of a two years ago  = x - 2 ,

age of b 2 years ago = y - 2 and

age of c two years ago = z - 2

Average age of a , b and c two years ago  = [ ( x - 2 ) + ( y - 2 ) + (z - 2 ) ] / 3

=>  Average age of a , b and c two years ago  = ( x + y + z - 6 ) / 3

given that Average age of a , b and c two years ago was 28

=> ( x + y + z - 6 ) / 3  = 28

=> x + y + z - 6 = 28 × 3

=> x + y + z - 6 = 84

=> x  + y + z = 84 +6

=> x = 90 - ( y + z )     ---------equation(1)

FOUR YEARS AGO

Age of b four years ago = present age of b - 4 = y - 4

Age of c four years ago = present age of c - 4 = z - 4

Average age of b and c 4 years ago  = [ ( y - 4 ) + ( z - 4 ) ] / 2

=> Average age of b and c 4 years ago  = (y + z - 8 )/ 2

As given that  Average age of b and c 4 years ago was 21

=> (y + z - 8 )/ 2  = 21

=> y + z - 8 = 42

=> y + z = 42 + 8

=> y + z = 50 ------------equation(2)

Now we have following two equations and we need current age of a that is x

x = 90 - ( y + z )     ---------equation(1)

y + z = 50 ------------equation(2)

Substituting value of y + z from equation(2) in equation(1) to get value of x

=>  x = 90 - 50 = 40

Hence age of a = x is 40 years

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