Question

The sum of two digits of a two digit number is 13.the difference between the digits of the number is 3.what is the two digit number?​

Answer 1

Answer:-

• The number we get will be 58.

Solution:-

Let:-

The digit at the unit place be b and the digit at the tenth place be a.

According to the question:-

We have:-

=> a + b = 13______(i)

As in the question it's not specified that which digit is greater either a or b so we have two cases :-

If a > b, Then Equation 2 we get will be

=> a - b = 3

Now upon adding these equation 1 & 2 we get

=> 2a = 16

=> a = 16/2

=> a = 8

And:-

=> b = a - 3

=> b = 8 - 3

=> b = 5

So:-

Here the number we get is 85.

If, a < b, then the equation 3 will be

=> b - a = 3

Now, upon adding equation 1 & 3 we get,

=> 2b = 16

=> b = 16/2

=> b = 8

And:-

=> a = b - 3

=> a = 8 - 3

=> a = 5

Therefore:-

Here the number we get will be 58.

Answer 2

To Find:-

• Find the two digit number.

Given:-

• The sum of two digits of a two digit number is 13.
• Difference between the digits of the number is 3.

Solution:-

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

So,

Let the first number be " x "

Second number be " y "

$\tt\implies \: x + y = 13 …… ( 1 )$

According to Question:-

$\tt\implies \: x - y = 3 …… ( 2 )$

Now by adding these two equations.

$\tt\implies \: x + y - x + y = 13 - 3$

$\tt\implies \: 2y = 10$

$\tt\implies \: y = 5$

By Substituting y in equation ( 1 ) we can find the value of x:-

$\tt\implies \: x + y = 13$

$\tt\implies \: x + 5 = 13$

$\tt\implies \: x = 13 - 5$

$\tt\implies \: x = 8$

Hence,

• $\tt\: Number = 85$