Question

A number consists of two digits. The sum of the digits is 15. If 27 is

subtracted from the number, its digits are interchanged. Find the number?​

Answer 1

Let the number be → 10x + y

In the 1st condition :—

• Sum of the digits → 15

$\color{red}{ \bold{ \underline{{x + y = 15}} \: \: - - - - (1)}}$

In the 2nd condition:—

• When 27 is subtracted from 10x + y , it becomes 10y + x .

${ \color{blue}{ \bold{10x + y - 27 = 10y + x}}}$

${ \color{blue}{ \bold{ \implies \: 9x - 9y = 27}}}$

${ \color{red}{ \bold{ \implies \: \underline{x - y = 3} \: \: \: - - - - - (2)}}}$

Now,

$\color{grey} \bold{ eq(1) - eq(2), }$

$\color{violet} \bold{ \implies \: x + y - (x - y) = 15 - 3}$

$\color{indigo} \bold{ \implies \: x + y - x + y = 12}$

$\color{indigo} \bold{ \implies 2 y = 12}$

$\color{blue} \bold{ \implies{ \boxed{ \bold{ y = 6}}}}$

Now, putting the value of y in eq(1) we get,

$\color{green}{ \bold{x + 6 = 15}}$

$\implies \: \boxed{ \color{purple}{ \bold{ x = 9}}}$

So, the number is

$\bold{10x + y }$

$= 10 \times 9 + 6$

$= 90 + 6$

$= \large \color{orange}{\bold{ 96}}$

$\Large{\colorbox{pink}{\underline{\underline{♠Answer♠:—\:\: 96}}}}$