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
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
Updated On: Jul 28, 2025
- 8000
- 6000
- 4000
- 2000
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
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.
Was this answer helpful?
0
0
Top Questions on Profit & Loss
- A person bought an item for Rs. 21000. He sold it for Rs. 18900. The loss percentage is
- A person bought an item for Rs. 1350 and spent Rs.150 towards transportation of the item. Then he sold it for Rs.1800. The profit percentage is
- A shopkeeper sold an article for Rs 3750. If he had charged 24% less, even then he would have earned a profit of 14%. What is the original cost of the article?
- By selling a table at Rs 475, a person loses 5%. To get a gain of 5%, he should sell the table for:
- A shopkeeper marks an article at such a price that after giving a discount of \(12\frac{1}{2}%\) on the marked price, he still earns a profit of 15%. If the cost price of the article is ₹385, then the marked price (in ₹) of the article will be:
- NPAT - 2021
- Quantitative Aptitude
- Profit & Loss
View More Questions
Questions Asked in CAT exam
- Let $a_n$ be the largest integer not exceeding $\sqrt{n}$. Then the value of $a_1 + a_2 + \dots + a_{50}$ is
- CAT - 2024
- Basics of Numbers
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Humans have managed to tweak the underlying biology of various plants and animals to produce high-tech crops and microbes. But regulating these entities is complicated, as the framework of policies and procedures are outdated and not flexible enough to adapt to emerging technology. The question is whether regulation will ever be able to keep up with human innovation, to regulate living things, which are apt to be unpredictable and unique; to capture all the potential risks when new biological entities are introduced, or when they pass on variations of their genes?- CAT - 2024
- Para Summary
- The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Different from individuals, states conduct warfare operations using the DIME model— “diplomacy, information, military, and economics.” Most states do everything they can to inflict pain and confusion on their enemies before deploying the military. In fact, attacks on vectors of information are a well-worn tactic of war and usually are the first target when the charge begins. It’s common for telecom data and communications networks to be routinely monitored by governments, which is why the open data policies of the web are so concerning to many advocates of privacy and human rights. With the worldwide adoption of social media, more governments are getting involved in low-grade information warfare through the use of cyber troops. According to a study by the Oxford Internet Institute in 2020, cyber troops are “government or political party actors tasked with manipulating public opinion online.” The Oxford research group was able to identify 81 countries with active cyber troop operations utilizing many different strategies to spread false information, including spending millions on online advertising.- CAT - 2024
- Para Summary
- The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Lyric poetry is a genre of private meditation rather than public commitment. The impulse in Marxism toward changing a society deemed unacceptable in its basic design would seem to place demands on lyric poetry that such poetry, with its tendency toward the personal, the small scale, and the idiosyncratic, could never answer. There is within Marxism, however, also a strand of thought that would locate in lyric poetry alternative modes of perception and description that call forth a vision of worlds at odds with a repressive reality or that draw attention to the workings of ideology within the hegemonic culture. The poetic imagination may indeed deflect larger social concerns, but it may also be implicitly critical and utopian.- CAT - 2024
- Para Summary
View More Questions