Question

1. The sum of the digits of a two digit number is 12. If the new number formed
by reversing the digits is greater than the original number by 18, find the
original number. Check your solution.​

Answer 1

SOLUTION:-

Given:

The sum of the digits of a two digit number is 12.

If the new number formed by reversing the digits is greater than the original number by 18.

To find:

The original number.

Solution:

Let the unit digit= x

Tens digit = 12 -x

⚫Original number= 10(12-x) +x

=) 120 - 10x +x

=) 120 -9x

Therefore,

Reversing the digits:

Unit digit = 12-x

Tens digit= x

⚫New number= 9x +12

As new number is less than the original number by 18.

=) 9x+12= 120-9x- 18

=) 9x+12= 102-9x

=) 9x + 9x = 102 -12

=) 18x = 90

=) x= 90/18

=) x= 5

Therefore,

Original number= 120 -9x

=) 120 - 9(5)

=) 120 - 45

=) 75

Thus,

The original number is 75.

Hope it helps ☺️