Question

A number consists of two digits whose sum is 16. If 18 is added to the number then the digits change their places. What is the number?​

Answer 1

Given

We have given sum of two digits number is 16

if 18 is added to the number then the digits change their places.

To Find

we have to find the number

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

let the one's place digit be x

then the ten's place digit be 16-x

So,number becomes => 10(16-x)+x

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$=>160-10x+x

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$=160-9x

Now,if the digits are reversed if 18 is added

then ,new number : 10x+16-x

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: => 9x+16$

According to the question:

=>160-9x+18=9x+16

=>160+18-16=9x+9x

=>162=18x

=>x=162÷18

=>x=9

given number :160-9x

=>160-9(9)

=>160-81

=>79

hence,the number is 79

Answer 2

Question :-

A number consists of two digits whose sum is 16. If 18 is added to the number then the digits change their places. What is the number?

Solution :-

Let one digit of the number be x , then it's tenth digits digits will be ( 16 - x ).

So, The given number is ,

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies10(16- x) + x$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 160 - 10x+ x$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 160 - 9x$

Now, If digits are reversed, then the number form is :

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies10 x + (16 - x)$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies10 x + 16- x$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies9x + 16$

Now, According to the question ,

If 18 is added to the number then the digits change their places.

So,

$\\ \: \: \: \sf \: \longrightarrow \: (160 - 9x) + 18 = 9x + 16$

$\\ \: \: \: \sf \: \longrightarrow \: 160 + 18 - 9x= 9x + 16$

$\\ \: \: \: \sf \: \longrightarrow \: 178 - 9x= 9x + 16$

$\\ \: \: \: \sf \: \longrightarrow \: 9x+ 9x= 178 - 16$

$\\ \: \: \: \sf \: \longrightarrow \: 18x= 162$

$\\ \: \: \: \sf \: \longrightarrow \: x= \dfrac{162}{18}$

$\\ \: \: \: \sf \: \longrightarrow \: \: \: \: \: \: \: \underline {\boxed{ { \color{blue}\frak{x= 9}}}}$

Therefore, The Given number is

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 160 - 9x$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 160 - 9 \times 9$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 160 - 81$

$\\ \: \: \: \sf \: \implies \: \: \: \: \: \: \: \underline {\boxed{ { \color{blue}\frak{the \: number \: = 79}}}}$

Hope it's helpful