Question

A two digit number such that the product of its digit is 15. If 18 is added to the number, the digits interchange their places. Find the number.

• A. 53
• B. 35
• C. 25
• D. 52

Answer 1

The correct option is B 35

Let the unit digit be x
Then, the tens digit will be $\frac{15}{x}$
According to the question,
$10\times \frac{15}{x}+x+18=10\times x+\frac{15}{x}$

$\Rightarrow 9\times \frac{15}{x}+18=9x$

$\Rightarrow x^2-2x-15=0$
$\Rightarrow x^2-5x+3x-15=0$
$\Rightarrow x(x-5)+3(x-5)=0$
$\Rightarrow (x-5)(x+3)=0$
$\Rightarrow x=5$ as digit cannot be negative
Hence, the number is 35
So, option b is correct.