Question

The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number ?

• A. 69
• B. 78
• C. 96
• D. Cannot be determined
• E. None of these

Answer 1

Answer: (A), (C)

69
96

Let the digits of the two digit number be x and y.

So the number can be xy or yx

from the question, we know

$x+y=15$ …….$\left(1\right)$

and $x-y=3$ …….$\left(2\right)$

solving these

Add $\left(1\right)+\left(2\right)$

$x+y=15$

+ $x-y=3$

$\overline{2x=18}$

$\therefore x=\frac{18}{2}=9$

Using $(x=9)$ in equation $\left(1\right)$

$x+y=15$

$9+y=15$

So $y=15-9=6$

$y=6$

So, $x=9$ & $y=6$

The digits can be $69$ or $96$.