Answer :

• The number whose sum of digits is 9 and when 27 is subtracted from it , the digits of the number is reversed is 63.

Explanation :

Given :

• Sum of the digits of the two-digt number = 9.

• When 27 is subtracted from the original number , the digits are reversed.

To find :

The number whose sum of digits is 9 and when 27 is subtracted from it , the digits of the number is reversed , Number = ?

Solution :

Let the digits of the two-digt number be a and b.

So,

• The original number is (10a + b) , and

• The number obtained on reversing the digits = (10b + a).

Now,

• Equation.(i)

According to the question , sum of digits of the two-digt number is 9 i.e,

⠀⠀⠀⠀⠀⠀⠀⠀⠀a + b = 9 ⠀⠀⠀⠀[Equation.(i)]

• Equation.(ii)

According to the question, when 27 is subtracted from the original number, the number is reversed i.e,

⠀⠀⠀⠀⠀⠀⠀⠀⠀(10a + b) - 27 = (10b + a)

By solving the above equation , we get :

==> (10a + b) - 27 = (10b + a)

==> (10a + b) - (10b + a) = 27

==> 10a + b - 10b - a = 27

==> 9a - 9b = 27

==> 9(a - b) = 27

==> a - b = 27/9

==> a - b = 3

∴ a - b = 3 ⠀⠀⠀⠀ [Equation.(ii)]

Now by adding Eq.(i) and Eq.(ii) , we get :

==> (a + b) + (a - b) = 9 + 3

==> (a + a) + (b - b) = 9 + 3

==> (a + a) + 0 = 9 + 3

==> (a + a) = 9 + 3

==> 2a = 12

==> a = 12/2

==> a = 6

∴ a = 6

Hence the value of a is 6.

Now by substituting the value of a in the Eq.(i) , we get :

==> a + b = 9

==> 6 + b = 9

==> b = 9 - 6

==> b = 3

∴ b = 3

Hence the value of b is 3.

By substituting the value of a and b in original number , we get :

==> 10a + b

==> (10 × 6) + 3

==> 60 + 3

==> 63

Therefore,

• The orginal number is 63.

Verified answer

Answer:

63

Step-by-step explanation:

the answer is 63.

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