Question

The sum of digits of two digit number is $4$. If the new number formed by reversing the digits is more than the original number by $18$. Find the original number.

• A. $10$
• B. $11$
• C. $12$
• D. $13$

Answer 1

The correct option is D $13$

Let $t$ = tens digit
$u$ = units digit
$10t$ + $u$ = value of the number
$10u$ + $t$ = value of the number with digits reversed
Two equations:
Sum of the digits is $4$
$t+u$ = $4$................ First Equation
Reversed number = original number + $18$
$10u+t=10t+u+18$
$9u-9t=18$
Divide by $9$
$u-t=$ $2$ Second equation
$u+t=$ $4$ First Equation
Add equations together
$2u$ = $6$
$u$ = $3$
$u+t$ = $4$
$3+t=4$
= $1$
Original number = $13$