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 or 85.

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 or 85.

Answer 2

$\underline{\underline{\green{\textbf{Step - By - Step - Explanation : -}}}}$

To Find :

• we need to find the two digit number

Solution :

$\red{\frak{Let}\begin{cases}\textsf{Units place Digit be y}\\\textsf{tens place digit be x} \end{cases}}$

Sum of digits = 13

›› x + y = 13

›› x = 13 - y .....(1)

Difference of digits = 3

›› x - y = 3

• From Equation (1)
• Substracting value of x from (1)

›› (13 - y) - y = 3

›› 13 - y - y = 3

›› 13 - 2y = 3

›› - 2y = 3 - 13

›› - 2y = -10

›› y = 10/2

›› y = 5

• Substracting value of y in (1)

›› x = 13 - y

›› x = 13 - 5

›› x = 8

Two digit number is : 10y + x

= 10 × 5 + 8

= 50 + 8

= 58

$\large\dag \large { \red{\underline{\bf{Hence }}}}$

• $\boxed{\underline{\pink{\textrm{Two Digit number is 58}}}}$

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