Question

The sum of the digits of a two digit number is 12. The number formed by interchanging the digits is greater than the original by 54. Find the original numbe​r​

Answer 1

ANSWER:-

Given:

The sum of the digits of a two digit number is 12.The number formed by interchanging the digits is greater than the original number.

To find:

The original number.

Solution:

Let the unit's digit be R. &

Let the ten's digit be M.

Therefore,

⚫Original number is 10M + R

⚫Reversed number is 10R + M.

According to the question:

⚫R+ M= 12

=) R= 12 - M.........(1)

So,

=) 10R+ M= 10M +R + 54

=) 10R - R+ M- 10M= 54

=) 9R - 9M= 54

=) R - M = 6

=) 12 - M -M = 6 [Using eq.(1)]

=) 12 - 2M = 6

=) -2M= 6 -12

=) -2M = -6

=) M= -6/-2

=) M= 3

Putting the value of M in equation (1), we get;

=) R = 12- 3

=) R= 9

Now,

⚫Original number:

=) 10M + R

=) 10(3)+ 9

=) 30 + 9

=) 39

Hence,

The original number is 39.

Hope it helps ☺️

Answer 2

Original number is 39