# A two-digit number whose sum of digits is 14. If 36 is added to the number, the digts are interchanged. How do you find the number?

Nov 21, 2016

Number is $59$

#### Explanation:

Let the unit's digit be $x$ as sum of digits is $14$, ten's digit is $14 - x$,

then the number is $10 \times \left(14 - x\right) + x$

i.e. $140 - 10 x + x$ or $140 - 9 x$

Reversing the digits number, unit digit becomes $14 - x$ and tens digit becomes $x$, hence number is $10 x + 14 - x = 9 x + 14$.

As adding $36$ to $140 - 9 x$ makes it $9 x + 14$, we have

$140 - 9 x + 36 = 9 x + 14$

or $176 - 14 = 9 x + 9 x$

or $18 x = 162$

or $x = 9$

and hence, unit''s digit is $9$ and tens digit is $5$

and number is $59$