Correct Answer - Option 4 : 73 and 37
Given :-
When you reverse the digits of age of father, you will get the age of son
One year ago the age of father was twice that of son's age
Calculation :-
Let the father's age with their digits be (10x + y) years
⇒ Age of son when reverse the digits of father's age = (10y + x) years
⇒ One year ago father age = (10x + y -1) years
⇒ One year ago son age = (10y + x -1) years
Now, from question
⇒ (10x + y - 1) = 2(10y + x - 1)
⇒ 10x + y - 1 = 20 y + 2x - 2
⇒ 10x - 2x - 1 + 2 = 20y - y
⇒ 8x + 1 = 19y ....(1)
Now
From option method
As option (1) and (3) is eliminate easily because here father age is less than son age so we can eliminate option (1) and (3)
Now from option 3rd,
When we take value of x = 3 and y =1
⇒ Age of father's = (10 × 3) + 1 = 31 years
⇒ Age of son = (10 × 1) + 3 = 13 years
Now,
⇒ One year ago father's age = (31 - 1) = 30 years
⇒ One year ago son age = (13 - 1) = 12 years
The above condition is not satisfied.
⇒ After put the value of x = 7 and y = 3 equation satisfied so
⇒ Age of father's = (10 × 7) + 3 = 73 years
⇒ Age of son = (10 × 3) + 7 = 37 years.
⇒ One year ago father's age = (73 - 1) = 72 years.
⇒ One year ago son age = (37 -1) = 36
It satisfied the condition given in question.
∴ Age of father and Age of son is 73 years and 37 years respectively.
