Question

The units digit of a two digit number is one more than double the tens digit. If digits are
interchanged the number obtained is 36 more than the original number. Find the number.​

Answer 1

Answer :

The required number = 37

Step-by-step explanation :

Given :

• The units digit of a two digit number is one more than double the tens digit.

• If digits are  interchanged the number obtained is 36 more than the original number.

To find :

the number

Solution :

Let

Units digit = y

Tens digit = x

Then the number will be = 10(x) + y = 10x + y

As given, units digit = 2(tens digit) + 1

⇒ y = 2x + 1

If the digits are interchanged, then the number has y in its tens digit and x in units digit

 The number = 10y + x

the number obtained is 36 more than the original number.

 10y + x = 36 + (10x + y)

 10y + x = 36 + 10x + y

  10y - y = 36 + 10x - x

   9y = 36 + 9x

   9y - 9x = 36

   9(y - x) = 9(4)

    y - x = 4

Substitute y = 2x + 1

 2x + 1 - x = 4

  x + 1 = 4

   x = 4 - 1

   x = 3

Tens digit = 3

Units digit = 2(3) + 1 = 7

So, the number = 37

 

Verification :

  The number = 37

If the digits are interchanged, then the number obtained = 73

Condition : the number obtained is 36 more than the original number

  73 = 37 + 36

  73 = 73

  LHS = RHS

Hence verified!