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Unit V Mathematical Reasoning And Aptitude
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Profit And Loss – Quiz 37
Profit And Loss Quiz 37 (10 MCQs)
This set of multiple-choice questions evaluates understanding of profit and loss calculations, including profit percentage, cost price, selling price, and financial forecasting. It covers basic arithmetic, trend identification, and the relationship between selling price and cost price, essential for financial statement analysis and future financial planning.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
Talal bought a toy for 50 SAR and he sold it next day for 75 SAR.Did he make a loss or a profit?
Show Answer
Correct Answer:
Correct answer is: A) Profit.
Exam Relevance:
SAT, ACT, GMAT, GRE
Difficulty:
Easy
Concept notes:
Profit is calculated as the selling price minus the cost price. If the selling price is higher than the cost price, a profit is made.
Common Mistakes:
A common mistake is to confuse profit with loss. Loss occurs when the selling price is lower than the cost price.
Explanations:
Talal bought the toy for 50 SAR and sold it for 75 SAR. The selling price (75 SAR) is higher than the cost price (50 SAR). Therefore, Talal made a profit.
Option Analysis:
Option A:
Correct. Talal made a profit because the selling price is higher than the cost price.
Option B:
Incorrect. Talal did not make a loss because the selling price is higher than the cost price.
2.
The shopkeeper makes a profit equal to the selling price of 5 shirts by selling 20 shirts. Find the percentage of his profit.
A) 25%.
B) 33 1/3%.
C) 5%.
D) 15%.
Show Answer
Correct Answer:
Correct answer is: (B) 33 1/3%.
Exam Relevance:
CAT, GMAT, GRE, SAT
Difficulty:
Moderate
Concept notes:
The problem involves understanding the relationship between profit and the selling price of items. The profit made is equal to the selling price of a certain number of items, which can be used to find the profit percentage.
Common Mistakes:
A common mistake is to confuse the profit with the cost price or to incorrectly calculate the profit percentage without considering the relationship between the profit and the selling price.
Explanations:
Let the cost price of one shirt be \( C \) and the selling price of one shirt be \( S \).
The profit made by selling 20 shirts is equal to the selling price of 5 shirts. Therefore, the profit from selling 20 shirts is \( 5S \).
The profit from selling 20 shirts can also be expressed as:
\[ \text{Profit} = 20S - 20C \]
Equating the two expressions for profit:
\[ 20S - 20C = 5S \]
Solving for \( S \):
\[ 20S - 5S = 20C \]
\[ 15S = 20C \]
\[ S = \frac{20C}{15} \]
\[ S = \frac{4C}{3} \]
The profit per shirt is:
\[ \text{Profit per shirt} = S - C = \frac{4C}{3} - C = \frac{4C - 3C}{3} = \frac{C}{3} \]
The profit percentage is:
\[ \text{Profit percentage} = \left( \frac{\text{Profit per shirt}}{\text{Cost price per shirt}} \right) \times 100 = \left( \frac{\frac{C}{3}}{C} \right) \times 100 = \left( \frac{1}{3} \right) \times 100 = 33 \frac{1}{3}\% \]
Option Analysis:
Option A:
25% is incorrect because the profit percentage is not 25%.
Option B:
33 1/3% is correct as calculated above.
Option C:
5% is incorrect because the profit percentage is not 5%.
Option D:
15% is incorrect because the profit percentage is not 15%.
3.
Cost price of 2 products is same.if first product sold for 20% profit and second product sold for 35% loss what is the overall profit or loss percentage?
A) 5% loss.
B) 10% loss.
C) 7.5% loss.
D) 7% loss.
Show Answer
Correct Answer:
Correct answer is: (C) 7.5% loss.
Exam Relevance:
CAT, GMAT, GRE, SAT, Competitive Exams
Difficulty:
Moderate
Concept notes:
The question involves calculating the overall profit or loss percentage when two products with the same cost price are sold at different profit and loss percentages.
Common Mistakes:
A common mistake is to simply average the profit and loss percentages, which would incorrectly yield a 7.5% profit or loss. However, the correct approach involves calculating the overall profit or loss based on the cost price.
Explanations:
Let the cost price of each product be \( C \).
1. The first product is sold at a 20% profit:
\[
\text{Selling Price of First Product} = C + 0.2C = 1.2C
\]
2. The second product is sold at a 35% loss:
\[
\text{Selling Price of Second Product} = C - 0.35C = 0.65C
\]
3. Total cost price for both products:
\[
\text{Total Cost Price} = C + C = 2C
\]
4. Total selling price for both products:
\[
\text{Total Selling Price} = 1.2C + 0.65C = 1.85C
\]
5. Overall profit or loss:
\[
\text{Overall Loss} = \text{Total Cost Price} - \text{Total Selling Price} = 2C - 1.85C = 0.15C
\]
6. Overall loss percentage:
\[
\text{Overall Loss Percentage} = \left( \frac{0.15C}{2C} \right) \times 100 = 7.5\%
\]
Thus, the overall loss percentage is 7.5%.
Option Analysis:
Option A:
5% loss is incorrect because the overall loss percentage is 7.5%.
Option B:
10% loss is incorrect because the overall loss percentage is 7.5%.
Option C:
7.5% loss is correct as calculated.
Option D:
7% loss is incorrect because the overall loss percentage is 7.5%.
4.
If the cost price of an item is $ 50 and the profit is 20%, what is the selling price?
A) $ 70.
B) $ 60.
C) $ 55.
D) $ 40.
Show Answer
Correct Answer:
Correct answer is: (B) $ 60.
Exam Relevance:
GMAT, GRE, CAT, SAT
Difficulty:
Easy
Concept notes:
The selling price is calculated by adding the profit to the cost price.
Common Mistakes:
A common mistake is to confuse the profit percentage with the selling price directly, without converting it to the actual profit amount.
Explanations:
To find the selling price, we first calculate the profit amount. The profit is 20% of the cost price. The cost price is $50. Therefore, the profit amount is:
\[ \text{Profit} = \frac{20}{100} \times 50 = 10 \]
Adding this profit to the cost price gives the selling price:
\[ \text{Selling Price} = 50 + 10 = 60 \]
Thus, the selling price is $60.
Option Analysis:
Option A:
$70 is incorrect because it is the result of adding 40% profit instead of 20%.
Option B:
$60 is correct as it is the result of adding 20% profit to the cost price.
Option C:
$55 is incorrect because it is the result of adding 10% profit instead of 20%.
Option D:
$40 is incorrect because it is less than the cost price, indicating a loss instead of a profit.
5.
If a product costs $ 50 to produce and is sold for $ 70, what is the profit?
A) $ 10.
B) $ 15.
C) $ 20.
D) $ 25.
Show Answer
Correct Answer:
Correct answer is: (C) $ 20.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Easy
Concept notes:
Profit is calculated as the selling price minus the cost price.
Common Mistakes:
A common mistake is to confuse profit with markup or to misinterpret the cost and selling prices.
Explanations:
To find the profit, subtract the cost price from the selling price. Here, the cost price is $50 and the selling price is $70. Therefore, the profit is $70 - $50 = $20.
Option Analysis:
Option A:
Incorrect, as $10 is not the correct profit.
Option B:
Incorrect, as $15 is not the correct profit.
Option C:
Correct, as $20 is the correct profit.
Option D:
Incorrect, as $25 is not the correct profit.
6.
Saritaben bought 18 chairs each at ' 700 and sold them all for ' 18900. What was the percentage of her profit or loss?
A) Profit was 50%.
B) Profit was 40%.
C) Profit was 55%.
D) Profit was 25%.
Show Answer
Correct Answer:
Correct answer is: (A) Profit was 50%.
Exam Relevance:
CAT, GMAT, GRE, SAT
Difficulty:
Easy
Concept notes:
The concept of profit percentage is calculated as the profit divided by the cost price, multiplied by 100.
Common Mistakes:
A common mistake is to confuse the profit percentage with the profit amount or to miscalculate the cost price or selling price.
Explanations:
1. Calculate the total cost price (CP) of the chairs:
\[
\text{CP} = 18 \times 700 = 12600
\]
2. The total selling price (SP) is given as 18900.
3. Calculate the profit:
\[
\text{Profit} = \text{SP} - \text{CP} = 18900 - 12600 = 6300
\]
4. Calculate the profit percentage:
\[
\text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 = \left( \frac{6300}{12600} \right) \times 100 = 50\%
\]
Thus, the profit percentage is 50%.
Option Analysis:
Option A:
Correct. The profit percentage is 50%.
Option B:
Incorrect. The profit percentage is not 40%.
Option C:
Incorrect. The profit percentage is not 55%.
Option D:
Incorrect. The profit percentage is not 25%.
7.
SP of book = Rs 410 loss = 120 find CP
A) 530.
B) 590.
C) 412.
D) 462.
Show Answer
Correct Answer:
Correct answer is: (A) 530.
Exam Relevance:
CAT, GMAT, GRE, SAT, Competitive Exams
Difficulty:
Easy
Concept notes:
In profit and loss problems, the cost price (CP) can be calculated using the selling price (SP) and the loss incurred. The formula to find CP when SP and loss are known is: CP = SP + Loss.
Common Mistakes:
A common mistake is to subtract the loss from the selling price instead of adding it, which would give an incorrect cost price.
Explanations:
Given:
- Selling Price (SP) = Rs 410
- Loss = Rs 120
To find the Cost Price (CP), we use the formula:
CP = SP + Loss
CP = 410 + 120
CP = 530
Thus, the cost price is Rs 530.
Option Analysis:
Option A:
530 (Correct)
Option B:
590 (Incorrect)
Option C:
412 (Incorrect)
Option D:
462 (Incorrect)
8.
Mrs. Bill sold her handbag for RM1,020.00 and lost RM80. Find the cost price of the bag.
A) RM1,100.
B) RM940.
C) RM1,200.
D) RM990.
Show Answer
Correct Answer:
Correct answer is: (A) RM1,100.
Exam Relevance:
SAT, GRE, GMAT, CAT
Difficulty:
Easy
Concept notes:
In profit and loss problems, the cost price (CP) can be calculated using the selling price (SP) and the loss incurred. The formula to find the cost price when a loss is incurred is: CP = SP + Loss.
Common Mistakes:
A common mistake is to subtract the loss from the selling price instead of adding it, which would give an incorrect cost price.
Explanations:
The selling price (SP) is RM1,020.00 and the loss incurred is RM80.00. To find the cost price (CP), we use the formula:
CP = SP + Loss
CP = RM1,020.00 + RM80.00
CP = RM1,100.00
Option Analysis:
Option A:
Correct. The cost price is RM1,100.00.
Option B:
Incorrect. This would be the cost price if the loss was added to the selling price incorrectly.
Option C:
Incorrect. This is not the correct calculation for the cost price.
Option D:
Incorrect. This is not the correct calculation for the cost price.
9.
A profit and loss account can help a business to?
A) Forecast.
B) Typecast.
C) Foretell.
D) Foreshadow.
Show Answer
Correct Answer:
Correct answer is: (A) Forecast.
Exam Relevance:
CPA, CFA, ACCA, CA
Difficulty:
Easy
Concept notes:
A profit and loss account provides a summary of a business's revenues, expenses, and net profit or loss over a specific period. This information can be used to predict future financial performance.
Common Mistakes:
A common misunderstanding is that a profit and loss account only shows past financial performance and cannot be used for future predictions.
Explanations:
A profit and loss account provides historical financial data, which can be analyzed to identify trends and patterns. These trends can then be used to forecast future financial performance. By understanding past revenues and expenses, a business can make informed decisions about future financial planning and budgeting.
Option Analysis:
Option A:
Correct. A profit and loss account can help a business forecast future financial performance based on historical data.
Option B:
Incorrect. Typecasting is not a relevant term in the context of financial statements.
Option C:
Incorrect. Foretelling is not a precise term for financial forecasting.
Option D:
Incorrect. Foreshadowing is not a relevant term in the context of financial statements.
10.
A person bought 50 pens for Rs 50 each. He sold 40 of them at a loss of 5%. He wants to gain 10% on the whole. Then his gain percent on the remaining pens should be
A) 15%.
B) 40%.
C) 50%.
D) 70%.
Show Answer
Correct Answer:
Correct answer is: (D) 70%.
Exam Relevance:
CAT, GMAT, GRE, SAT
Difficulty:
Hard
Concept notes:
To solve this problem, we need to calculate the total cost price, the total selling price required for a 10% gain, and then determine the required selling price for the remaining pens to achieve this overall gain.
Common Mistakes:
A common mistake is to assume that the loss on the first 40 pens and the gain on the remaining 10 pens will balance out to achieve the overall 10% gain. This is incorrect because the overall gain is calculated on the total cost price, not on individual segments.
Explanations:
1. Calculate the total cost price (CP) of 50 pens:
\[
\text{Total CP} = 50 \times 50 = 2500 \text{ Rs}
\]
2. Calculate the total selling price (SP) required for a 10% gain:
\[
\text{Total SP} = 2500 \times 1.10 = 2750 \text{ Rs}
\]
3. Calculate the selling price of the first 40 pens at a 5% loss:
\[
\text{CP of 40 pens} = 40 \times 50 = 2000 \text{ Rs}
\]
\[
\text{SP of 40 pens} = 2000 \times 0.95 = 1900 \text{ Rs}
\]
4. Calculate the required selling price of the remaining 10 pens to achieve the total SP of 2750 Rs:
\[
\text{SP of remaining 10 pens} = 2750 - 1900 = 850 \text{ Rs}
\]
5. Calculate the gain percent on the remaining 10 pens:
\[
\text{CP of 10 pens} = 10 \times 50 = 500 \text{ Rs}
\]
\[
\text{Gain} = 850 - 500 = 350 \text{ Rs}
\]
\[
\text{Gain percent} = \left(\frac{350}{500}\right) \times 100 = 70\%
\]
Option Analysis:
Option A:
15% is incorrect because it does not account for the required overall gain of 10%.
Option B:
40% is incorrect because it does not account for the required overall gain of 10%.
Option C:
50% is incorrect because it does not account for the required overall gain of 10%.
Option D:
70% is correct as it is the gain percent required on the remaining 10 pens to achieve the overall 10% gain.
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Frequently Asked Questions
What is the difference between cost price and selling price?
The cost price is the amount paid to acquire or manufacture an item, while the selling price is the amount at which the item is sold to a customer.
How is profit percentage calculated?
Profit percentage is calculated by dividing the profit by the cost price and then multiplying by 100 to get a percentage.
What is the purpose of a profit and loss account?
A profit and loss account summarizes the revenues, costs, and expenses incurred during a specific period to determine the net profit or loss.
How can historical financial data be used in financial forecasting?
Historical financial data can be analyzed to identify trends and patterns, which can then be used to make informed predictions about future financial performance.
What skills are necessary to understand profit and loss calculations?
Basic arithmetic skills, understanding of financial terms, and the ability to interpret financial statements are essential for understanding profit and loss calculations.