Question

The age of my son a equals the sum of the four digits of my car number. My car number is also divisible by 11, which incidentally happens to be my son b's age. When i subtract a's age from the car number, i get 1962, the year my daughter c was born. What is my car number?

Answer 1

Let my car number = a b c d

My son's age (a)= a + b+ c +d

As my car number is also divisible by 11.

→That is[ sum of digits at even or odd places - Sum of  digits at  odd or even  places] will be divisible by 11.

→[(a+c) - (b +d)] will be divisible by 11.

→ a b c d - (a+b+c+d)= 1962

→ a b c d- a's age = 1962(c's age)

→ a b c d= a's age + 1962

→→ a b c d= [1962 + A number (a)]→→Divisible by 11

Substituting , values of a that is from 0, 1,2,3,4,5,6,....9,..

I found that when, a=7,→→a b c d=1962 + 7= 1969, which is divisible by 11.

Sum of digits at even places = 1+6=7

Sum of digits at odd places = 9 +9=18

Difference = 18-7=11 , which is divisible by 11.

So, the four digit number = 1969

Your son's age = 1+9+6+9= 7 years