Question

The number of solutions of the equation $\frac{x}{7}=\left\{x\right\}$ is
(where {.} is the fractional part function)

• A. $0$
• B. $1$
• C. $6$
• D. $7$

Answer 1

Answer: (C)

$6$

$\frac{x}{7}=\left\{x\right\}$
We know that, $0\le \left\{x\right\}<1$
$\Rightarrow 0\le \frac{x}{7}<1$
$\Rightarrow 0\le x<7...\left(1\right)$


When $x\in [6,7)$
$\frac{x}{7}=x-6$
$\Rightarrow x=7$
which is not possible from eqn$\left(1\right)$
Therefore, the given equation has $6$ solutions.