Question

The digits of a two digit number differ by 5. If the digits are interchanged and the
resulting number is added to the original number, we get 77. Find the original number.
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Answer 1

Heya!!

Any two digit number say ( ab ) can be written as 10a + b

=>

Let the required number be xy

ACCORDING TO THE QUESTION

x - y = 5 .... Equation ( i )

And

10x + y + 10y + x = 77

Becoz original number is 10x + y And the number obtained by interchanging the digits is 10y + x

=>

11x + 11y = 77

=>

x + y = 7 .... Equation ( ii )

Now, Add both the Equations ( i and ii ) we get

2x = 12

x = 6 And y = 1

So, the origin number is 10×6 + 1 = 61