Question

The digit of a two digit number differ by 3. If the digits are interchange and the resulting number is added to the original number we get 143. What can be the original number?

Answer 1

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Let us assume, the x is the tenth place digit (for example x=3 in the two digit number 32) and y is the unit place digit of the two-digit number(for example y=2 in the two digit number 32). Also assume x > y

Therefore,

the two-digit number is 10x + y(310+2=32) and reversed number is 10y + x(210+3=23);

Given that The digit of a two digit number differ by 3, it can be written as:

x - y = 3.....................(1)

Also given the digits are interchange and the resulting number is added to the original number we get 143, it can be written as:

10x + y + 10y + x = 143

11x + 11y = 143

x + y = 13 ...............(2)

Adding equation (1) and equation (2) ;

then we get

2x = 16

x = 8

then the value of x is put in equation (1),we get;

y = x - 3

= 8 - 3

= 5

Therefore, the two-digit number = 10x + y

= (10 8) + 5

= 85