Question

If we interchange d digits in the age of father . We get age of his son the numbers digits in age of father & son is a natural number. If the sum of father & his son is 55 years. Find their present age​

Answer 1

The present age of the father is 41 years, and the present age of his son is 14 years.

• Age of father will be a two digit number.

Let the digit in the units' place be y, and the digit in the tens' place be x.

=> The present age of father is 10x + y.

• On interchanging the digits in father's age, we get the age of the son.

=> The age of the son = 10y+ x

• According to the question,

(10x + y) + (10y + x) = 55

Or, 10x + y + 10y + x = 55

Or, 11x + 11y = 55

Or, 11 ( x + y ) = 55

Or, x + y = 55 / 11

Or, x + y = 5

• Since x + y = 5, and it is given that the digits in the ages of both father and son are natural numbers, the possible values of x and y are :

x = 1, y = 4

x = 2, y = 3

x = 3, y = 2

x = 4, y = 1

(Natural numbers are numbers from 0 to ∞ )

• Therefore, the possible ages of  father and son are :

(i) Father : 10x + y = (10 × 1) + 4 = 10 + 4 = 14

Son's age = Reverse of 14 = 41 (Not possible)

(ii) Father : 10x + y = (10 × 2) + 3 = 20 + 3 = 23

Son's age = Reverse of 23 = 32 (Not possible)

(iii) Father : 10x + y = (10 × 3) + 2 = 30 + 2 = 32

Son's age = Reverse of 32 = 23 (Possible)

But, 32 - 23 = 9, the difference between a father and son's age cannot be so small, so this possibility is also rejected.

(iv) Father : 10x + y = (10 × 4) + 1 = 40 + 1 = 41

Son's age = Reverse of 41 = 14 (Possible)

41 - 14 = 27, the difference between a father and son's age can be 27, hence, this possibility is correct.

• Therefore, present age of father = 41 years.

Present age of son = 14 years.