Let the ages of Mr. Naidu, Mrs. Naidu and Shrinivas be

*x*,

*y* and

*z* respectively on January 01, 1989.

*x* −

*y* =

*z*Let

*a* be the number of years that have elapsed between 1989 and Mr. Naidu turning 35.

After 10 years, Mr. Naidu will be 45. Also, Mrs. Naidu will be

*y’* + 10 and Shrinivas will be

*z’* + 10.

We know from the condition in the statement that

∴

*z’*^{2} − 2z’ = 48

∴ (

*z’* − 8)(

*z’* + 6) = 0

∴

*z’* = 8 or

*z’* = −6

But the age cannot be negative and so

*z’* = 8.

∴

*y’* = 32 while

*x’* = 35

Now,

*x* –

*y* =

*x’* –

*y’* = 3 =

*z*Also,

*z* +

*a* =

*z’*

∴

*z’* –

*z* =

*a* = 5

∴

*y* =

*y’* –

*a* = 32 – 5 = 27

∴ On Janaury 01, 1989, Mrs. Naidu was 27 years old. On January 01, 2014, she would be (27 + 25) = 52 years old.

Hence, option 4.