Question

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the sum of the digits of a two digit number is 11 the number obtained by interchanging the digits exceeds the original number by 27 find the number

Answer 1

$\textbf{\huge{ Hello Mate! }}$

Let the number be 10y + x.

When we interchange digits its mean that x and y will replace the place.

We will get, 10x + y.

Hence by forming equation we get,

10x + y = 10y + x + 27

9x - 9y = 27

9( x - y ) = 27

x - y = 3 ___(1)

As its given in question that x + y = 11 ___(2)

By adding (1) and (2) we get,

2x = 14

x = 7

Substituting value of x in eq (2)

7 + y = 11

y = 4

Since, our original number was 10y + x so

= 10 × 4 + 7

= 40 + 7 = 47

$\textsf{\red{ Hence original number 47 }}$

$\textbf{ Have great future ahead! }$