Question

the sum of the digit number is 12 also nine time this numer is twice the number obtained by reversing the order of the digit find the number​

Answer 1

Appropriate Question:

The sum of the digits of a two digit number is 12.Also nine times this number is twice the number obtained by reversing the order of the digit.Find the number.

Given:

•The sum of the digits of the two digit number is 12.

•This number is nine times is twice the number obtained by reversing the digit.

To Find:

•Find the number

Solution:

The sum of the digits of the two digit number is 12 and after reversing the digit the real number is nine times is twice the number and we are said to find numbers.

Let's assume:

• Let the ten's digit number be x
• one's digit number be y.

So the number formed will be = 10x+ y

Given: x+y=12. ---------------(i)

12(10x+y) = 2(10y + x) -----------(ii)

120x + 12y = 20y + 20x

120x - 20x = 20y -12y

100x = 8y

100x-8y = 0 ---------(ii)

Now solve the equation (i) and (ii)

x +y = 12 ------(i)

100x -8y = 0 -------(ii)

_________________

Here we can see that no any number is cancel out so from equation (ii) take 8 and multiple it in equation (i)

8x +8y = 48 ---------(i) × 8

100x - 8y = 0 --------(ii)

__________________

92x = 48

x = 48/92

x = 12/23

After getting the value of x now find y on putting equation (i)

x + y = 12

12/23 + y = 12

y = 12 -12/23

y = 264/23

On solving (i) and (ii) simultaneously we will get x = 12/23 and y = 264/23.

The number is ( 10x +y)= 384/23

Answer 2

Correct Question :

• The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Given :

• The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits.

To find :

• Find the number.

Solution :

Let ,

The ten digit number be x

and

1 digit number be y

So,

$\sf The \: number \: will \: be = \red{10x + y}$

Given that,

1st method :

x + y = 9

2nd method :

9 ( 10x + y ) = 2 ( 10y + x )

⟹ 88 x - 11 y = p

On solving this two methods , We will get x = 1 and y = 8

$\sf\underbrace\red{ \: \: ∴ \: The \: number \: is \: 18}$