Question

A number consist of two digits whose sum is 9. If 27 is subtracted from the original number , its digits are interchanged. find the original number?​

Answer 1

Answer:

36 is the original no .

Explanation:

Let the unit’s digit be x

And the ten’s digit = (9 – x)

∴ Number = 10 × (9 – x) + x

→ 90 – 10x + x = (90 – 9x)

Adding 27 to the number 90 – 9x, we get 117 – 9x

Number with digits interchanged is

10x + (9 – x) = 9x + 9

→ 117 – 9x = 9x + 9

→ 9x + 9x = 117 - 9

→ 18x = 108

→ x = 108/18

= 6

Now, Unit digit = x = 6

tens digit = 9 - x

= 9 - 6

= 3

Hence, 36 is the original no. .

Answer 2

Answer:

$\bigstar{\bold{Original\:number=63}}$

Explanation:

$\Large{\underline{\rm{Given:}}}$

• Sum of the digits = 9
• If 27 is subtracted from the original number, the digits are interchanged.

$\Large{\underline{\rm{To\:Find:}}}$

• The original number

$\Large{\underline{\rm{Solution:}}}$

↬ Here we have to find the original number.

↬ Let us assume the ten's digit of the number as x.

↬ Let us assume the unit's digit of the number as y.

↬ By given,

    x + y = 9

    x = 9 - y -------(1)

↬ Now the number is given by,

   Original number = 10x + y

↬ Also,

    Reversed number

↬ Now by given,

   Original number - 27 = Reversed number

↬ Substitute the data,

    10x + y - 27 = 10y + x

↬ Substitute the value of x from equation 1

    10(9 - y) + y - 27 = 10y + 9 - y

    90 - 10y + y - 27 = 9y + 9

    63 - 9y = 9y + 9

    9y + 9y = 63 - 9

    18y = 54

        y = 54/18

        y = 3

↬ Hence the unit's digit of the number is 3.

↬ Substitute the value of x in equation 1

    x = 9 - 3

    x = 6

↬ Therefore the ten's digit of the number is 6.

↬ Hence the number is given by,

    Original number = 10 × 6 + 3

    Original number = 63

↬ Therefore the original number is 63.

   

    $\boxed{\bold{Original\:number=63}}$

$\Large{\underline{\rm{Verification:}}}$

Unit's digit + Ten's digit = 9

6 + 3 = 9

9 = 9

Original number - 27 = Reversed number

63 - 27 = 36

36 = 36

↬ Hence verified.