Given that, Mukesh purchased $10$ bicycles in $2017$, all at the same price.
Let $x$ be the purchase price (cost price) of one bicycle.
Then, the price of $10$ bicycles is $10x.$
He sold six bicycles at a profit of $25\% .$
- Selling price of $6$ bicycles $=6x \times \frac {125}{100}= \frac {15x}{2}$
He sold the remaining $4$ bicycles at a loss of $25\%$
- Selling price of $4$ bicycles $= 4x \times \frac {75}{100}=3x$
Total selling price of $10$ bicycles $= \frac {15x}{2} + 3x= \frac {15x+6x}{2}= \frac {21x}{2}$
$ \boxed {\text {profit = selling price – cost price} }$
$2000= \frac{21x}{2} – 10x$
$ \Rightarrow 2000 = \frac {21x-20x}{2}$
$ \Rightarrow 2000 = \frac {x}{2}$
$ \Rightarrow x= 4000 $
$\therefore$ Mukesh purchased a bicycle in Rs. $4000$
Correct Answer: C