Question

A number when divided by a certain divisor leaves a remainder of $12$ What is the divisor if a remainder of $9$ is left when thrice the same number is divided by the same divisor?

• A. $18$
• B. $24$
• C. $27$
• D. $30$

Answer 1

The correct option is C $27$

Let divisor be $d$

then number,

$\Rightarrow$ $a=bd+12$

Now, $3a=cd+9$

$\hookrightarrow$ a constant

$\Rightarrow$ Or $3a=3d+36$

by multiplying equation $\left(1\right)$ by $3$

$\Rightarrow$ Or $0=d(c-3)-27$

$\Rightarrow$ $d(c-3)=27$

$\Rightarrow$ $d$ is a factor of $27$ from ption $d=27.$

Hence, the answer is $27.$