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If the present age of D is 54 years.
The age of B is 6 years younger than D.
present age of B = 54-6 = 48 years
The average of the present ages of A, B, C and D is (y-3) years.
Sum of the present ages of A, B, C and D = 4(y-3)
present age of A + present age of B + present age of C + present age of D = 4(y-3)
present age of A+48+present age of C+54 = 4(y-3)
12 years hence, the ratio between the ages of A and C is 9:8 respectively.
Let’s assume 12 years hence, the ages of A and C are ‘9a‘ and ‘8a‘ respectively.
(9a-12)+48+(8a-12)+54 = 4(y-3) Eq.(i)
(i) 12
Put the possible value of ‘y’ in Eq.(i).
(9a-12)+48+(8a-12)+54 = 4x(12-3)
(9a-12)+48+(8a-12)+54 = 4x9
17a+78 = 36
Here the value of ‘a’ will be negative. So this is not the possible value of ‘y’.
(ii) 24
Put the possible value of ‘y’ in Eq.(i).
(9a-12)+48+(8a-12)+54 = 4x(24-3)
17a+78 = 4x21
17a = 84-78 = 6
Here the value of ‘a’ will be in fractions. So this is not the possible value of ‘y’.
(iii) 36
Put the possible value of ‘y’ in Eq.(i).
(9a-12)+48+(8a-12)+54 = 4x(36-3)
17a+78 = 4x33
17a+78 = 132
17a = 132-78
17a = 54
Here the value of ‘a’ will be in fractions. So this is not the possible value of ‘y’.
(iv) 48
Put the possible value of ‘y’ in Eq.(i).
(9a-12)+48+(8a-12)+54 = 4x(48-3)
17a+78 = 4x45
17a+78 = 180
17a = 180-78
17a = 102
a = 6
Here the value of ‘a’ is a natural number. So this is the only possible value of ‘y’.
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