Question

a number consist of two digits if the number is formed by reversing its digiys is added to it sum is 88 anf if the reversed number is subtracted from original number the result is 36 find the number​

Answer 1

Answer:

Original number = 62

Step-by-step explanation:

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

• If a two digit number and the reversed number is added the sum is 88
• If the reversed number is subtracted from the original number , the result is 36.

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

• The original number

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

➔ Let the ten's digit of the number be x.

➔ Let the unit's digit of the number be y

➔ Hence,

    The number = 10x + y

➔ Now the reversed number is given by,

    Reversed number = 10y + x

➔ By given,

   Original number + Reversed number = 88

    10x + y + 10y + x = 88

    11x + 11y = 88

➔ Dividing by 11,

    x + y = 8

    x = 8 - y-----(1)

➔ Also by given,

    Original number - Reversed number = 36

    10x + y - (10y + x) = 36

➔ Substitute value of x from equation 1,

    10 (8 - y) + y - (10y + 8 - y) = 36

    80 - 10y + y - 9y - 8 = 36

    -18y = 36 - 72

    -18 y = -36

    y = 2

➔ Hence one's digit of the number is 2.

➔ Substitute the value of y in equation 1,

    x = 8 - 2

    x = 6

➔ Hence the ten's digit of the number is 6.

➔ Therefore,

    Original number = 10 × 6 + 2 = 62

➔ Hence the original number is 62.

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

➔ Original number + Reversed number = 88

    62 + 26 = 88

    88 = 88

➔ Original number - Reversed number = 36

    62 - 26 = 36

    36 = 36

➔ Hence verified.