Question

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

• A. 8000
• B. 6000
• C. 4000
• D. 2000

Answer 1

The Correct Option is C

Let the purchase price of each bicycle be Rs. \( x \).

Total cost price of 10 bicycles = \( 10x \). 

Step 1: Calculate the selling price of bicycles sold at a profit
6 bicycles sold at a profit of 25%.
The cost price of 6 bicycles = \( 6x \).
Selling price of 6 bicycles = \( 6x + 0.25 \times 6x \) = \( 6x \times 1.25 = 7.5x \).

Step 2: Calculate the selling price of bicycles sold at a loss
4 bicycles sold at a loss of 25%.
The cost price of 4 bicycles = \( 4x \).
Selling price of 4 bicycles = \( 4x - 0.25 \times 4x \) = \( 4x \times 0.75 = 3x \).

Step 3: Calculate the total selling price and profit
Total selling price = Selling price of 6 bicycles + Selling price of 4 bicycles = \( 7.5x + 3x = 10.5x \).
Total profit gained = Total selling price - Total cost price
Total profit = \( 10.5x - 10x = 0.5x \).

Given that the total profit is Rs. 2000,

\( 0.5x = 2000 \)

Solving for \( x \):

\( x = \frac{2000}{0.5} = 4000 \).

Thus, the purchase price of each bicycle is Rs. 4000.