Age Calculation using Calendar

Given information:
The sum of ages of a father and his son is 52. The father was born in 1923.

To find:
The birth year of the son.

Solution:
Let the age of the son be x.
According to the given information, the sum of ages of father and son is 52.
Hence, the age of the father is (52 – x).

We know that the father was born in 1923.
So, his age in the year x will be (x – 1923).

Similarly, the age of the son in the year x will be (x – year of birth of son).

According to the question, the sum of ages of the father and son in the year x is 52.
Hence, we can form the equation as follows:
(x – 1923) + (x – year of birth of son) = 52
Simplifying the equation, we get:
2x – year of birth of son = 1995
year of birth of son = 2x – 1995

Now, we need to find the value of x such that the age of the son is an integer.
From the given options, we can substitute the values of x one by one and check which option satisfies the condition.

Option (a): x = 24
year of birth of son = 2x – 1995 = 2(24) – 1995 = –1947
The year of birth of the son is negative. Hence, option (a) is not correct.

Option (b): x = 26
year of birth of son = 2x – 1995 = 2(26) – 1995 = –1943
The year of birth of the son is negative. Hence, option (b) is not correct.

Option (c): x = 26
year of birth of son = 2x – 1995 = 2(26) – 1995 = 1947
The year of birth of the son is a positive integer. Hence, option (c) is correct.

Option (d): x = 29
year of birth of son = 2x – 1995 = 2(29) – 1995 = 1951
The year of birth of the son is greater than the given year. Hence, option (d) is not correct.

Therefore, the birth year of the son is 1949, which corresponds to option (c).