Question

Form the equation if the sum of the two digits of a two digit number is 9. If9 is added to the number, the
digits are reversed, find the number.​

Answer 1

Answer:

45

Step-by-step explanation:

Let the number be ab(=10a + b). In the same manner as 54 = 5(10) + 4, 47 = 4(10) + 7, etc.

Sum of digits = a + b = 9         ...(1)                      

When 9 is added, digits are reversed,

⇒ 10a + b + 9 = ba(= 10b + a)

⇒ 10a + b + 9 = 10b + a

⇒ 9a - 9b = - 9

⇒ a - b = - 1                        ...(2)

  Using, (1) and (2),

⇒ (a + b) + (a - b) = 9 + (-1)

⇒ 2a = 8     ⇒ a = 4

 Thus, a + b = 9    ⇒ b = 5

Number is ab(=10a + b) = 45

Answer 2

Answer:

45

Step-by-step explanation:

Let the number be ab(=10a + b). In the same manner as 54 = 5(10) + 4, 47 = 4(10) + 7, etc.

Sum of digits = a + b = 9         ...(1)                      

When 9 is added, digits are reversed,

⇒ 10a + b + 9 = ba(= 10b + a)

⇒ 10a + b + 9 = 10b + a

⇒ 9a - 9b = - 9

⇒ a - b = - 1                        ...(2)

  Using, (1) and (2),

⇒ (a + b) + (a - b) = 9 + (-1)

⇒ 2a = 8     ⇒ a = 4

 Thus, a + b = 9    ⇒ b = 5

Number is ab(=10a + b) = 45