Question

Sum of digits of two digit number is 13. Number obtained by interchanging digits of given number exceeds by 27. Find the number

Answer 1

Answer:

Let us consider that the two digits are a and b.

Then the number is (10a + b).

When the digits are interchanged, the new number is (10b + a).

By the given condition :

a + b = 13 .....(i)

and

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

=> 9b = 9a + 27

=> b = a + 3 .....(ii)

Putting b = a + 3 in (i), we get :

a + a + 3 = 13

=> 2a = 10

=> a = 5

From (ii), putting a = 5, we get :

b = 5 + 3 = 8

Therefore, the number is 58.

Answer 2

Given:-

• The sum of the two digits number of a two digits number is 13.
• The number obtained by interchanging the digit of a given number is less than number by 27.

To find:-

• Find the original number ..?

Solutions:-

• Let the digits at unit's place be y.
• Let the digit at ten's place be x.

Number => 10x + y

The sum of the two digits number of a two digits number is 13.

=> x + y = 13 .....(i).

The number obtained by interchanging the digit of a given number is less than number by 27.

=> 10y + 5

Number obtained by reversing the digits.

=> 10x + y - 27

=> 10y + x = 10x + y - 27

=> 27 = 10x + y - 10y - x

=> 27 = 9x - 9y

=> 27 = 9(x - y)

=> 27/9 = x - y

=> 3 = x - y

Putting the value of x from Eq (i). in Eq (ii).

=> x + y = 13

=> 3 + y + y = 13

=> 2y = 13 - 3

=> 2y = 10

=> y = 10/2

=> y = 5

Putting the value of y in Eq (i).

=> x + 5 =13

=> x = 13 - 5

=> x = 8

So, Number = 10x + y

=> 10(8) + 5

=> 85

Hence, the original number is 85.