Question

sum of the digits of a 2 digit number is 11. the given number obtained by interchanging the digit by 9 . find the number.
​

Answer 1

Correct Question :-

The sum of a 2 digit number is 11. If the number obtained by reversing the digit is 9 less than the original number, what is the number ?

Answer:-

Let the digit at ten's place be x and digit at one's place be y .

So, the number = 10x + y

Given:

Sum of the digits = 11

⟶ x + y = 11

⟶ x = 11 - y -- equation (1)

Also given that,

The number formed by reversing the digits is 9 less than the original number.

⟶ Reversed number = Original number - 9

• Reversed number = 10y + x.

So,

⟶ 10y + x = 10x + y - 9

⟶ 10y + x - 10x - y = - 9

Substitute the value of x from equation (1).

⟶ 10y + 11 - y - 10(11 - y) - y = - 9

⟶ 9y + 11 - 110 + 10y - y = - 9

⟶ 18y = - 9 - 11 + 110

⟶ 18y = 90

⟶ y = 90/18

⟶ y = 5

Substitute the value of y in equation (1).

⟶ x = 11 - y

⟶ x = 11 - 5

⟶ x = 6

The number = 10(6) + 5 = 60 + 5 = 65.

∴ The required two digit number is 65.

Answer 2

Answer:

Solution :-

Let, ten's digits be x

And, unit digits be y

Hence, The number will be 10x + y

If obtaining by reversing the digits = 10y + z

According to the question,

=> 10x + y - (10y + x) = 9

=> 10x + y - 10y - x = 9

=> 9x - 9y = 9

Now, dividing each terms with "9" we get,

=> x - y = 1 ..... Equation no 1

Given,

==>x + y = 11 ..... Equation no (1)

==> y = 11 - x ........ Equation no (2)

By adding Equation no 1 and 2 we get,

=> 2x = 12

=> x = $\dfrac{12}{2}$

=> x = 6

By putting x = 6 in the equation no 2 we get,

=> y = 11 - 6

=> y = 5

$\therefore$ The number will be,

=> 10x + y

=> 10 × 6 + 5

=> 65

Hence the required number will be 65 .