Question

Sum of two digit no. is 8. When we interchange the digits, It is found that the resulting new no. is greater than original no. by 28. What is two digit number???​

Answer 1

Answer:

30

Step-by-step explanation:

Let the unit digit of a two-digit number be x.

Therefore, ten's place digit = 8 - x.

So, original number = 10(8 - x) + x

Given, Resulting new number is greater than original by 28.

⇒ 10x + (8 - x) = 10(8 - x) + x + 28

⇒ 10x + 8 - x = 80 - 10x + x + 28

⇒ 18x = 100

⇒ x = 50/9

Hence, 2 digit number = 10(8 - x) + x

                                      = 10(22/9) + 50/9

                                      = 220/9 + 50/9

                                      = 30.

∴ Two-digit number = 30.

Hope it helps!

Answer 2

$\textsf{\underline {\Large {Correct Question}}}$ :

Sum of two digits of a number is 8. When we interchange the digits, it is found that the resulting new number is greater than original number by 28. What is two digit number???​

$\textsf{\underline {\Large {Solution}}}$ :

Let the one's digit be x and ten's digit be y.

Then, the two digit number formed = 10y + x

According to the question,

Sum of their digits ( x and y ) = 8

$\mathsf{x\:+\:y\:=\:8}$

$\mathsf{x\:=\:8\:-\:y}$ --> ( i )

On interchanging the digits, The resulting number = 10x + y

Also,

( 10x + y ) is greater than ( 10y + x ) by 28.

$\mathsf{(\:10x\:+\:y\:)\:-\:(\:10y\:+\:x\:)\:=\:28}$

$\mathsf{\:10x\:+\:y\:-\:10y\:-\:x\:=\:28}$

$\mathsf{9x\:-\:9y\:=\:28}$

From equation ( i ), Putting value of x,

$\mathsf{9(\:8\:-\:y\:) \:-9y\:=\:28}$

$\mathsf{72\:-\:9y\:-9y\:=\:28}$

$\mathsf{-18y\:=\:28\:-\:72}$

$\mathsf{-18y\:=\:44}$

$\mathsf{y\:=\:{\dfrac{22}{9}}}$

Putting value of y in equation ( i ),

$\mathsf{x\:=\:8\:-\:y}$

$\mathsf{x\:=\:8\:-\:{\dfrac{22}{9}}}$

$\mathsf{x\:=\:{\dfrac{72\:-\:22}{9}}}$

$\mathsf{x\:=\:{\dfrac{50}{9}}}$

➡️ Two digit number = $\mathsf{10y\:+\:x\:=\:{\dfrac{220}{9}} \:+\:{\dfrac{50}{9}}}$

➡️ Two digit number = $\mathsf{\dfrac{270}{9}}$

➡️ Two digit number = $\boxed{\mathsf{30}}$