Question

the sum of the digit of a certain two digit number is 7 reversing is digit increases the number by 9 what is the number

Answer 1

$\huge\boxed{\textbf{34}}$
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Let the digit in tens place be be $\bf{x}$
And, Let the digit in units place be be $\bf{x}$

So, the number will be $\bf{10x + y}$
Also, the number obtained by reversing the digital will be $\bf{10x + y}$
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A.T.Q,

$\bf{x + y = 7 -----(1)}$

$\bf{10x + y + 7 = 10y + x}$
=> $\bf{9x - 9y = -7 -----(2)}$

Multiplying equation(1) by 9 and then adding it to equation (2) we get,

=> $18x = 54$

=> $\frac{54}{18}$

=> $\boxed{\textbf{x = 3}}$

Substituting value of x in equation(1) we get,

=> $3 + y = 7$

=> $y = 7 - 3$

=> $\boxed{\textbf{y = 4}}$
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Hence, the number is 10(3) + 4.

=> 30 + 4
=> 34