Question

The sum of unit place and tens place digits of a two digit number is $12$. If the new number formed by reversing those digits is less than the original number by $18$. Find the original number.

• A. $70$
• B. $75$
• C. $80$
• D. $85$

Answer 1

The correct option is B $75$

Let the unit place digit $=x$
Ten's place digit $=12-x$
Original number $=$ $10\times (12-x)+x$
$=120-10x+x$
$=120-9x$
Reversing the digit:
Unit digit $=12-x$
Ten's digit $=x$
New number formed $=$ $10\times x+12-x$
$=9x+12$
As new number is less than the original number by $18$
New number $=$ original number $-18$
$9x+12=120-9x-18$
$18x=120-30$
$18x=90$
$x=5$
Original number $=120-9x$
$=120-9\times 5$
$=120-45$
$=75$
Original number $=75.$