Question

If the number obtained by interchanging the digits of a two digit number is 18 more than the original number and the sum of the digits is 8 then what is the original number ?​

Answer 1

Solution -

Let the original number be 10a + b.

Then, 'a' is the tens digit and 'b' is the units digit.

Since the sum of digits is 8, therefore,

a + b = 8, i.e., b = 8 - a.

So, the original number is 10a + ( 8 - a ).

Therefore, the number obtained by interchanging the digits is 10(8 - a) + a, and so we have

{10(8 - a) + a} - {10a + (8-a)} = 18

Solving the equation, we get

a = 3.

And so, b = 8 - a = 8 - 3 = 5.

Hence, the original number is

10a + b = 30 + 5 = 35.

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