Question

The sum of the digits in a two - digit number is 6.
If we add 18 to that number , we get a number consisting of the same digits written in the reverse order . Find the number .​

Answer 1

Question:-

• The sum of the digits in a two - digit number is 6 . If we add 18 to that number , we get a number consisting of the same digits written in the reverse order . Find the number .

Given:-

• The sum of the digits in a two - digit number is 6 . If we add 18 to that number we get numbers consisting of the same digits written in the reverse order .

To Find:-

• Find the number .

Solution:-

• Let the first digit be " x "

• Second digit be " y "

So ,

The number is

• 10y + x

After reversing the number then the number is 10x + y

According to the Question:-

$\tt\implies \: 10x + y - 10y - x = 18$

$\tt\implies \: 9x - 9y = 18$

$\tt\implies \: 9( x - y ) = 18$

$\tt\implies \: x - y = \cancel\dfrac { 18 } { 9 }$

$\tt\implies \: x - y = 2 . . . . . ( 1 )$

Here ,

It's also given as x + y = 6 . . . . ( 2 )

Solve the two equations:-

$\tt\implies \: x - y + x + y = 2 + 6$

$\tt\implies \: 2x = 8$

$\tt\implies \: x = 4$

Substitute " x " in equation ( 1 ):-

$\tt\implies \: x - y = 2$

$\tt\implies \: 4 - y = 2$

$\tt\implies \: y = 2$

Therefore ,

The number is

$\tt\implies \: 10y + x$

$\tt\implies \: 10( 2 ) + 4$

$\tt\implies \: 20 + 4$

$\tt\implies \: 24$

Hence ,

• The number is 24 .

Answer 2

Solution -

The sum of the digits in a two digit number is 6.

Let the number be ab.

Sum of digits -

> a + b = 6

Adding 18 to the number ; the digits are reversed .

So

> ab + 18 = ba

> 10a + b + 18 = 10b + a

> 9a - 9b = -18

> a - b = -2

> a = b - 2

Now , a + b = 6

> ( b - 2) + b = 6

> 2b = 8

> b = 4.

a = 2.

The number is 24.

This is the required answer !

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