Question

The digit of a two digit number are in the ratio 2 ratio 3 and the number obtained by interchanging the digits is greater than the original number by 27 what is the original number?

Answer 1

Answer:

69

Solution:

Here ,

It is given that ;

The digit of a two digit number are in the ratio 2:3.

Thus,

Let the tens digit of original number be 2x and the unit digit be 3x .

Thus,

The original number = 10•2x + 1•3x

= 20x + 3x

= 23x

Now,

On interchanging the digits of original numer , The tens digit of the new number will be 3x and the unit digit will be 2x .

Thus,

The number obtained by interchanging the digits of original numer = 10•3x + 1•2x

= 30x + 2x

= 32x

According to the question ,

The number obtained by interchanging the digits is greater than the original number by 27.

Thus,

=> New no. = original no. + 27

=> 32x = 23x + 27

=> 32x - 23x = 27

=> 9x = 27

=> x = 27/9

=> x = 3

Hence,

Tens digit of original numer = 2x

= 2•3

= 6

Unit digit of original numer = 3x

= 3•3

= 9

Hence ,

The original numer is 69 .