Question

The ten's digit of a two-digit number is twice its unit's digit.
The number obtained by interchanging the digits is 36 less
than the original number. Find the original number.​

Answer 1

Given:

• The tens digit of a two - digit number is twice the units digit .
• The number obtained by interchanging the digits is 36 less than the original number.

To Find:

• The original number.

How to solve?

• We will firstly suppose the units and tens digit as variables .Then we will frame two linear equⁿ s and solve then simultaneously to get the values of variables .Lastly we will put the respective values to find the Original Number.

Answer:

Given that the tens digit of a two - digit number is twice the units digit and the number obtained by interchanging the digits is 36 less than the original number.

So firstly let us take :

• Units digit be x .
• Tens digit be y .

As per given condition y = 2x. ..........(i)

♠ Original Number ♠

= 10×y + x = 10y + x .

♠ Reversed Number ♠

Here x will be tens digit while y will become units digit.

= 10 × x + y = 10x+y .

Now it is given that the Reversed Number is 36 less than the original Number .This means that the difference of Original Number and Reversed Number is 36.

Lets frame a equⁿ :

⇒ ( 10y+x ) - ( 10x+y ) = 36 .

⇒ 10y + x - 10x - y = 36.

⇒ 9y - 9x = 36.

⇒ 9 ( y - x ) = 36.

⇒ ( y - x ) = 36/9.

⇒ y - x = 4.

⇒ 2x - x = 4. [ From equⁿ (i) ]

⇒ x = 4.

Hence the units digit of the Number is 4 .

Lets substitute this value in equⁿ (i) :—

⇒ y = 2x.

⇒ y = 2 × 4.

⇒ y = 8.

Hence Original Number was 10y+x =10×8+4=80+4=84.

Hence the Original Number is 84.

Answer 2

Let ,

Original number be " 10x + y "

Unit's digit = " y "

Then , ten's digit (x) = " 2y "

According to the question ,

10y + x = 10x + y - 36

9y - 9x = -36

9x - 9y = 36

x - y = 4

2y - y = 4

y = 4

$\therefore$

• Unit's digit = 4
• Ten's digit = 8
• Original number = 84