Question

The difference between a two digit number and the number obtained by interchanging the digits is 72. What is the difference between the digits of the number? ( A ) 7 ( B ) 6 ( C ) 5 ( D ) 8

Answer 1

Answer:

Option D is correct.

Step-by-step explanation:

Let-:

The two numbers be in the form

10x + y that is the original number

and

The reverse of the number is 10y + x.

Then-:

According to Question

=> (10x + y) - (10y + x) = 72

=> 10x + y -10y - x = 72

=> 10x - x -10y + y = 72

=> 9x - 9y=72

=> x - y = 8

Therefore:-

The difference of the two digits is 8.

Answer 2

Answer:

Option (D)8 is correct option.

Let the tens place of two digit number be x.

The unit place of two digit number be y.

Original number = 10x+y

Number obtained by interchanging the digits = 10y+x

$\: \: \: \: \: \: \: (10x + y) - (10y + x) = 72 \\ = > 10x + y - 10y - x = 72 \\ = > 9x - 9y = 72 \\ = > 9(x -y ) = 72 \\ = > (x - y) = \frac{72}{9 } \\ = >( x - y) = 8$

Hence, difference between the digits of the number = 8