Question

A two digit number N contains the smaller of the two digits in the unit place. The product of the digit is 40 and the difference between the digit is 3. The sum of the digit in N is_____.

• A. 11
• B. 12
• C. 13
• D. 14

Answer 1

The correct option is C 13

Let two numbers are $a$ and $b$

Now given,

$a\times b=40...\left(1\right)$
$a-b=3....\left(2\right)$

From eq2
$\Rightarrow a=3+b$
Now put the value of a in eq 1

$\Rightarrow (3+b)\times b=40$
$\Rightarrow b^2+3b=40$
$\Rightarrow b^2+3b-40=0$

Now factorizing the equation
$\Rightarrow b^2+8b-5b-40=0$
$b(b+8)-5(b+8)=0$
$\Rightarrow (b+8)(b-5)=0$
We have two values of b
$\Rightarrow b=-8,5$

We take positive value $b=5$
Now place the value in eq2
$\Rightarrow a-5=3$
$\Rightarrow a=8$

Sum of these two digits
$\Rightarrow a+b\Rightarrow 8+5=13$