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A shopkeeper (from cloth shop) has a magic metre scale whose length keeps on changing on an hourly basis. In the first hour, its length reduced to 0.8 m and in the second hour, its length is increased to 1.2 m then again in the third hour its length reduces to 0.8 m and so on. One day, at 9 a.m., the shopkeeper opened the shop. The length of the scale at that point of time was 0.8 m. The shopkeeper closed the shop on that day at 7 p.m. In the first hour, only 1 customer came. The number of customers coming to the shop increased by 1 each hour. Each of the customers bought 10 m cloth. At 7 p.m., the shopkeeper counted all the money gained in that day. What is the percentage loss or profit to the shopkeeper? [Note: If you ignore fluctuations caused by the ruler, the shopkeeper sells at cost price]
  • a)
    4% profit
  • b)
    10% loss
  • c)
    5.55% loss
  • d)
    1.79% loss
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A shopkeeper (from cloth shop) has a magic metre scale whose length ke...
From 9 am to 7 pm, the numbers of customers that visited the shop = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
Assume that the cost of the cloth is Rs. 100 per metre.
Total length of the cloth sold (according to the shopkeeper) = 55 x 10 = 550 m
Actual length of the cloth sold = [(1 + 3 + 5 + 7 + 9) x 10 x 0.8] + [(2 + 4 + 6 + 8 + 10) x 10 x 1.2] = 560 m
There is a loss of 10 m cloth overall in that day.
Percent loss = (10 x 100) / 560 = 1.79 Hence, option 4.
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Most Upvoted Answer
A shopkeeper (from cloth shop) has a magic metre scale whose length ke...
Given:
- Length of the scale keeps changing on an hourly basis.
- In the first hour, the length reduced to 0.8 m.
- In the second hour, the length increased to 1.2 m.
- In the third hour, the length reduced to 0.8 m again.
- This pattern continues throughout the day.

Plan:
1. Calculate the total length of the scale at the end of the day.
2. Calculate the total cloth sold by each customer.
3. Calculate the total amount of money gained by the shopkeeper.
4. Calculate the cost price for the shopkeeper.
5. Calculate the profit/loss percentage.

Calculation:
1. Total length of the scale at the end of the day:
- The length of the scale changes every 2 hours, so it goes from 0.8 m to 1.2 m and back to 0.8 m.
- There are 12 hours in a day, so the scale goes through this cycle 6 times.
- Total length = 0.8 m + 1.2 m + 0.8 m + ... (6 times)
- Total length = (0.8 + 1.2) * 6 = 12 m

2. Total cloth sold by each customer:
- Each customer buys 10 m of cloth.
- The number of customers increases by 1 each hour.
- The total cloth sold can be calculated using the formula for the sum of an arithmetic series.
- Total cloth sold = (First term + Last term) * Number of terms / 2
- First term = 10 m (for the first customer)
- Last term = 10 m + (Number of customers - 1) * 10 m
- Number of terms = Number of customers
- Total cloth sold = (10 + (10 + (Number of customers - 1) * 10)) * Number of customers / 2

3. Total amount of money gained by the shopkeeper:
- The shopkeeper sells at cost price, so the amount gained is equal to the cost price.
- Total money gained = Total cloth sold * Cost price per meter
- Cost price per meter = 1 (since the shopkeeper sells at cost price)
- Total money gained = Total cloth sold * 1

4. Cost price for the shopkeeper:
- The cost price is the total length of the scale.
- Cost price = Total length of the scale = 12 m

5. Profit/loss percentage:
- Profit/Loss = Total money gained - Cost price
- Profit/Loss percentage = (Profit/Loss / Cost price) * 100
- Profit/Loss = Total money gained - Cost price = Total cloth sold - Total length of the scale
- Profit/Loss percentage = (Total cloth sold - Total length of the scale) / Total length of the scale * 100
- Profit/Loss percentage = [(10 + (10 + (Number of customers - 1) * 10)) * Number of customers / 2 - 12] / 12 * 100

Calculating the Profit/Loss Percentage:
- Number of customers at 7 p.m. = 7 (since the shop closes at 7 p.m.)
- Profit/Loss percentage = [(10 + (10 +
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A shopkeeper (from cloth shop) has a magic metre scale whose length keeps on changing on an hourly basis. In the first hour, its length reduced to 0.8 m and in the second hour, its length is increased to 1.2 m then again in the third hour its length reduces to 0.8 m and so on. One day, at 9 a.m., the shopkeeper opened the shop. The length of the scale at that point of time was 0.8 m. The shopkeeper closed the shop on that day at 7 p.m. In the first hour, only 1 customer came. The number of customers coming to the shop increased by 1 each hour. Each of the customers bought 10 m cloth. At 7 p.m., the shopkeeper counted all the money gained in that day. What is the percentage loss or profit to the shopkeeper? [Note: If you ignore fluctuations caused by the ruler, the shopkeeper sells at cost price]a)4% profitb)10% lossc)5.55% lossd)1.79% lossCorrect answer is option 'D'. Can you explain this answer?
Question Description
A shopkeeper (from cloth shop) has a magic metre scale whose length keeps on changing on an hourly basis. In the first hour, its length reduced to 0.8 m and in the second hour, its length is increased to 1.2 m then again in the third hour its length reduces to 0.8 m and so on. One day, at 9 a.m., the shopkeeper opened the shop. The length of the scale at that point of time was 0.8 m. The shopkeeper closed the shop on that day at 7 p.m. In the first hour, only 1 customer came. The number of customers coming to the shop increased by 1 each hour. Each of the customers bought 10 m cloth. At 7 p.m., the shopkeeper counted all the money gained in that day. What is the percentage loss or profit to the shopkeeper? [Note: If you ignore fluctuations caused by the ruler, the shopkeeper sells at cost price]a)4% profitb)10% lossc)5.55% lossd)1.79% lossCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A shopkeeper (from cloth shop) has a magic metre scale whose length keeps on changing on an hourly basis. In the first hour, its length reduced to 0.8 m and in the second hour, its length is increased to 1.2 m then again in the third hour its length reduces to 0.8 m and so on. One day, at 9 a.m., the shopkeeper opened the shop. The length of the scale at that point of time was 0.8 m. The shopkeeper closed the shop on that day at 7 p.m. In the first hour, only 1 customer came. The number of customers coming to the shop increased by 1 each hour. Each of the customers bought 10 m cloth. At 7 p.m., the shopkeeper counted all the money gained in that day. What is the percentage loss or profit to the shopkeeper? [Note: If you ignore fluctuations caused by the ruler, the shopkeeper sells at cost price]a)4% profitb)10% lossc)5.55% lossd)1.79% lossCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A shopkeeper (from cloth shop) has a magic metre scale whose length keeps on changing on an hourly basis. In the first hour, its length reduced to 0.8 m and in the second hour, its length is increased to 1.2 m then again in the third hour its length reduces to 0.8 m and so on. One day, at 9 a.m., the shopkeeper opened the shop. The length of the scale at that point of time was 0.8 m. The shopkeeper closed the shop on that day at 7 p.m. In the first hour, only 1 customer came. The number of customers coming to the shop increased by 1 each hour. Each of the customers bought 10 m cloth. At 7 p.m., the shopkeeper counted all the money gained in that day. What is the percentage loss or profit to the shopkeeper? [Note: If you ignore fluctuations caused by the ruler, the shopkeeper sells at cost price]a)4% profitb)10% lossc)5.55% lossd)1.79% lossCorrect answer is option 'D'. Can you explain this answer?.
Solutions for A shopkeeper (from cloth shop) has a magic metre scale whose length keeps on changing on an hourly basis. In the first hour, its length reduced to 0.8 m and in the second hour, its length is increased to 1.2 m then again in the third hour its length reduces to 0.8 m and so on. One day, at 9 a.m., the shopkeeper opened the shop. The length of the scale at that point of time was 0.8 m. The shopkeeper closed the shop on that day at 7 p.m. In the first hour, only 1 customer came. The number of customers coming to the shop increased by 1 each hour. Each of the customers bought 10 m cloth. At 7 p.m., the shopkeeper counted all the money gained in that day. What is the percentage loss or profit to the shopkeeper? [Note: If you ignore fluctuations caused by the ruler, the shopkeeper sells at cost price]a)4% profitb)10% lossc)5.55% lossd)1.79% lossCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of A shopkeeper (from cloth shop) has a magic metre scale whose length keeps on changing on an hourly basis. In the first hour, its length reduced to 0.8 m and in the second hour, its length is increased to 1.2 m then again in the third hour its length reduces to 0.8 m and so on. One day, at 9 a.m., the shopkeeper opened the shop. The length of the scale at that point of time was 0.8 m. The shopkeeper closed the shop on that day at 7 p.m. In the first hour, only 1 customer came. The number of customers coming to the shop increased by 1 each hour. Each of the customers bought 10 m cloth. At 7 p.m., the shopkeeper counted all the money gained in that day. What is the percentage loss or profit to the shopkeeper? [Note: If you ignore fluctuations caused by the ruler, the shopkeeper sells at cost price]a)4% profitb)10% lossc)5.55% lossd)1.79% lossCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A shopkeeper (from cloth shop) has a magic metre scale whose length keeps on changing on an hourly basis. In the first hour, its length reduced to 0.8 m and in the second hour, its length is increased to 1.2 m then again in the third hour its length reduces to 0.8 m and so on. One day, at 9 a.m., the shopkeeper opened the shop. The length of the scale at that point of time was 0.8 m. The shopkeeper closed the shop on that day at 7 p.m. In the first hour, only 1 customer came. The number of customers coming to the shop increased by 1 each hour. Each of the customers bought 10 m cloth. At 7 p.m., the shopkeeper counted all the money gained in that day. What is the percentage loss or profit to the shopkeeper? [Note: If you ignore fluctuations caused by the ruler, the shopkeeper sells at cost price]a)4% profitb)10% lossc)5.55% lossd)1.79% lossCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A shopkeeper (from cloth shop) has a magic metre scale whose length keeps on changing on an hourly basis. In the first hour, its length reduced to 0.8 m and in the second hour, its length is increased to 1.2 m then again in the third hour its length reduces to 0.8 m and so on. One day, at 9 a.m., the shopkeeper opened the shop. The length of the scale at that point of time was 0.8 m. The shopkeeper closed the shop on that day at 7 p.m. In the first hour, only 1 customer came. The number of customers coming to the shop increased by 1 each hour. Each of the customers bought 10 m cloth. At 7 p.m., the shopkeeper counted all the money gained in that day. What is the percentage loss or profit to the shopkeeper? [Note: If you ignore fluctuations caused by the ruler, the shopkeeper sells at cost price]a)4% profitb)10% lossc)5.55% lossd)1.79% lossCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A shopkeeper (from cloth shop) has a magic metre scale whose length keeps on changing on an hourly basis. In the first hour, its length reduced to 0.8 m and in the second hour, its length is increased to 1.2 m then again in the third hour its length reduces to 0.8 m and so on. One day, at 9 a.m., the shopkeeper opened the shop. The length of the scale at that point of time was 0.8 m. The shopkeeper closed the shop on that day at 7 p.m. In the first hour, only 1 customer came. The number of customers coming to the shop increased by 1 each hour. Each of the customers bought 10 m cloth. At 7 p.m., the shopkeeper counted all the money gained in that day. What is the percentage loss or profit to the shopkeeper? [Note: If you ignore fluctuations caused by the ruler, the shopkeeper sells at cost price]a)4% profitb)10% lossc)5.55% lossd)1.79% lossCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A shopkeeper (from cloth shop) has a magic metre scale whose length keeps on changing on an hourly basis. In the first hour, its length reduced to 0.8 m and in the second hour, its length is increased to 1.2 m then again in the third hour its length reduces to 0.8 m and so on. One day, at 9 a.m., the shopkeeper opened the shop. The length of the scale at that point of time was 0.8 m. The shopkeeper closed the shop on that day at 7 p.m. In the first hour, only 1 customer came. The number of customers coming to the shop increased by 1 each hour. Each of the customers bought 10 m cloth. At 7 p.m., the shopkeeper counted all the money gained in that day. What is the percentage loss or profit to the shopkeeper? [Note: If you ignore fluctuations caused by the ruler, the shopkeeper sells at cost price]a)4% profitb)10% lossc)5.55% lossd)1.79% lossCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.
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