Question

The sum of digits of a two-digit number is 15. The original number is reversed. The reversed number is greater than original number by 9. Find the original number.​

Answer 1

Answer:

$\bigstar{\bold{The\:number=78}}$

Step-by-step explanation:

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

• Sum of the digits of the number = 15
• Reversed number = Original number + 9

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

• The original number

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

→ Let the ten's digit be x and the unit's digit be y

→ By given, we know that

  x + y = 15

  x = 15 - y -----(1)

→ Here the number is,

  Number = 10 x + y

→ Therefore the reversed number is,

  Reversed number = 10 y + x

→ By given we knoe that

  10y + x = 10x + y + 9

→ Substitute the value of x from equation 1

  10y + 15 - y = 10 (15 - y) + y + 9

  9y + 15 = 150 - 10y + y + 9

  9y + 15 = 159 - 9y

  18y = 144

      y = 144/18

      y = 8

→ Hence the unit's digit of the number is 8

→ Substituting value of y in equation 1

  x = 15 - 8

  x = 7

→ The ten's digit of the number is 7

→ Therefore,

   The number = 10 x + y

   The number = 10 × 7 + 8

   The number = 70 + 8 = 78

$\boxed{\bold{The\:number=78}}$

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

→ x + y = 15

  7 + 8 = 15

  15 = 15

→ 10y + x = 10x + y + 9

  10 ×8 + 7 = 10 × 7 + 8 + 9

  80 + 7 = 70 + 17

  87 = 87

→ Hence verified.