Question

a certain number of 2 digit is four times the sum of its digits and it's 45 it is added to its the digit will be reversed find the number​

Answer 1

Answer:

$\red\bigstar \boxed{\sf The \: Required \: Number \: is \:510}$

PLEASE NOTE:-

✳There is a slight correction in your question.

Corrected Question

A certain number of 3 digit is four times the sum of its digits and it's 45 it is added to its the digit will be reversed find the number​ ?

✩ SOLUTION  ✩

Let us assume that the digit in the tens place of that number is 'x'.

Let us assume that the digit in the unit place of that number is 'y'.

Condition - 1

A certain number of 2 digit is four times the sum of its digits.

$\implies$

10x + y = 4 (x+y)

$\implies$

10x + y = 4x + 4y

$\implies$

10x - 4x = 4y - y

$\implies$

6x = 3y

$\implies$

2x = y $\longrightarrow$ (1)

Condition - 2

If 45 is added to its the digit will be reversed.

$\implies$

10x + y + 45 = 10y + x

$\implies$

10 y - y + x - 10x = 45

$\implies$

9y - 9x = 45

{Dividing Throughout by 9}

$\implies$

y - x = 5

Let us Substitute the value of y = 2x from (1) in this equation.

$\implies$

2x - x = 5

$\implies$

x = 5

From(1) we know that y = 2x

$\implies$

y = 2 × 5 = 10