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Mukesh purchased $10$ bicycles in $2017$, all at the same price. He sold six of these at a profit of $25\%$ and the remaining four at a loss of $25\%$. If he made a total profit of Rs.$2000$, then his purchase price of a bicycle, in Rupees, was  ________

1. $8000$
2. $6000$
3. $4000$
4. $2000$

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. $4000$

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