Question

A certain number of two digit is three times the sum of the digits. If 45 is added to it, the digits are reversed. Find the numbers.​

Answer 1

Answer:

$\bigstar{\bold{Original\:number=27}}$

$\bigstar{\bold{Reversed\:number=72}}$

Step-by-step explanation:

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

• A number =  3 times the sum of the digits
• If 45 is added to it, the digits are reversed

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

• The numbers

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

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

➦ Let us aasume the ten's digit of the number as x

➦ Hence,

    The number = 10x + y

➦ By given

    The number =  3 × sum of digits

     10x + y = 3 (x + y)

     10x + y = 3x + 3y

     10x - 3x = 3y - y

     7x = 2y

        y = 7x/2 -----(1)

➦ Also by given,

    The number + 45 = Reversed number

    10x + y + 45 = 10y + x

    10x - x + 45 = 10y - y

     9x + 45 = 9y

➦ Divide the whole equation by 9

    x + 5 = y

➦ Substitute the value of y from equation 1

    x + 5 = 7x/2

    2x + 10 = 7x

    2x - 7x = -10

     5x = 10

       x = 10/5

       x = 2

➦ Hence the ten's digit of the number is 2

➦ Substitute the value of x in equation 1

    y = 7 × 2/2

    y = 7

➦ Hence the unit's digit of the number = 7

➦ Therefore the original number is,

    Original number = 10x + y

    Original number = 10 × 2 + 7

    Original number = 27

    $\boxed{\bold{Original\:number=27}}$

➦ Now the reversed number is given by,

    Reversed number = 10y + x

    Reversed number = 10 × 7 + 2

    Reversed number = 72

    $\boxed{\bold{Reversed\:number=72}}$

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

➦ Number =  3 × sum of the digits

    27 =  3 × (2 + 7)

    27 = 3 × 9

    27 = 27

➦ Original Number + 45 = Reversed number

    27 + 45 = 72

    72 = 72

➦ Hence verified.