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Unit V Mathematical Reasoning And Aptitude
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Profit And Loss – Quiz 12
Profit And Loss Quiz 12 (10 MCQs)
This set of multiple-choice questions evaluates the ability to calculate cost price, selling price, profit, and loss. It covers concepts such as cost per unit, profit percentage, loss percentage, and revenue per unit. The questions test skills in solving linear equations, basic arithmetic, and financial calculations related to profit and loss.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
With the correct words. Word Bank: profit, cost, selling price, cost, profit. To find the profit, subtract the ..... from the selling price.
A) Cost.
B) Wages.
C) Ingredients.
D) Tax.
Show Answer
Correct Answer:
Correct answer is: (A) Cost.
Exam Relevance:
GMAT, GRE, SAT, ACT, CAT
Difficulty:
Easy
Concept notes:
Profit is calculated by subtracting the cost from the selling price.
Common Mistakes:
A common mistake is to confuse profit with other financial terms such as wages, ingredients, or tax.
Explanations:
To find the profit, you need to subtract the cost from the selling price. The cost represents the expenses incurred to produce or acquire the product, while the selling price is the amount at which the product is sold. The difference between these two values gives the profit.
Option Analysis:
Option A:
Correct. The cost is subtracted from the selling price to find the profit.
Option B:
Incorrect. Wages are not directly related to the calculation of profit.
Option C:
Incorrect. Ingredients are part of the cost but not the term used in the profit formula.
Option D:
Incorrect. Tax is not directly involved in the basic profit calculation.
2.
A fruit seller sells apples at the rate of Rs. 9per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%?
A) 12.
B) 11.81.
C) 11.
D) 11.32.
Show Answer
Correct Answer:
Correct answer is: (B) 11.81.
Exam Relevance:
CAT, GMAT, GRE, Banking Exams
Difficulty:
Moderate
Concept notes:
The concept involves calculating the selling price required to achieve a desired profit percentage, given the current selling price and loss percentage.
Common Mistakes:
A common mistake is to incorrectly calculate the cost price or to use the wrong formula for profit or loss percentage.
Explanations:
1. First, determine the cost price (CP) of the apples. Given that the seller sells apples at Rs. 9 per kg and incurs a loss of 20%, we can use the formula:
\[
\text{Selling Price (SP)} = \text{CP} \times (1 - \text{Loss Percentage})
\]
\[
9 = \text{CP} \times (1 - 0.20)
\]
\[
9 = \text{CP} \times 0.80
\]
\[
\text{CP} = \frac{9}{0.80} = 11.25
\]
2. Next, calculate the selling price (SP) required to achieve a 5% profit. Use the formula:
\[
\text{SP} = \text{CP} \times (1 + \text{Profit Percentage})
\]
\[
\text{SP} = 11.25 \times (1 + 0.05)
\]
\[
\text{SP} = 11.25 \times 1.05 = 11.8125
\]
3. Therefore, the selling price per kg to achieve a 5% profit is approximately Rs. 11.81.
Option Analysis:
Option A:
12. This is incorrect as the calculated selling price is approximately 11.81.
Option B:
11.81. This is the correct answer as it matches the calculated selling price.
Option C:
11. This is incorrect as the calculated selling price is approximately 11.81.
Option D:
11.32. This is incorrect as the calculated selling price is approximately 11.81.
3.
SP = Rs. 85, Profit = Rs. 20, CP =?
A) Rs. 65.
B) Rs. 105.
C) Rs. 110.
D) Rs. 60.
Show Answer
Correct Answer:
Correct answer is: (A) Rs. 65.
Exam Relevance:
CAT, GMAT, GRE, SAT, Competitive Exams
Difficulty:
Easy
Concept notes:
The cost price (CP) can be calculated using the formula: CP = SP - Profit.
Common Mistakes:
A common mistake is to confuse the formula for calculating CP with the formula for calculating SP, which is SP = CP + Profit.
Explanations:
Given:
- Selling Price (SP) = Rs. 85
- Profit = Rs. 20
Using the formula for cost price:
CP = SP - Profit
CP = 85 - 20
CP = 65
Therefore, the cost price (CP) is Rs. 65.
Option Analysis:
Option A:
Rs. 65. (Correct)
Option B:
Rs. 105. (Incorrect)
Option C:
Rs. 110. (Incorrect)
Option D:
Rs. 60. (Incorrect)
4.
The difference between a loss of 13% and a profit of 15% was ' 63. The cost price of the item is:
A) 225.
B) 207.
C) 198.
D) 243.
Show Answer
Correct Answer:
Correct answer is: (A) 225.
Exam Relevance:
CAT, GMAT, GRE, Bank PO, SSC CGL
Difficulty:
Moderate
Concept notes:
The difference between a loss of 13% and a profit of 15% is given as Rs. 63. We need to find the cost price of the item.
Common Mistakes:
A common mistake is to incorrectly calculate the percentage difference or to confuse the profit and loss percentages.
Explanations:
Let the cost price (CP) of the item be \( x \).
Loss of 13% means the selling price (SP) is \( 0.87x \).
Profit of 15% means the selling price (SP) is \( 1.15x \).
The difference between the selling prices is given as Rs. 63:
\[ 1.15x - 0.87x = 63 \]
\[ 0.28x = 63 \]
\[ x = \frac{63}{0.28} \]
\[ x = 225 \]
Thus, the cost price of the item is Rs. 225.
Option Analysis:
Option A:
225 (Correct)
Option B:
207 (Incorrect)
Option C:
198 (Incorrect)
Option D:
243 (Incorrect)
5.
If an object is bought for $ 90 and then sold for a loss of 15%. How much was it sold for?
A) $ 103.50.
B) $ 80.
C) 75.
D) $ 76.50.
Show Answer
Correct Answer:
Correct answer is: (D) $ 76.50.
Exam Relevance:
GMAT, GRE, CAT, SAT
Difficulty:
Moderate
Concept notes:
The concept of loss in profit and loss calculations involves reducing the cost price by the percentage of loss to find the selling price.
Common Mistakes:
A common mistake is to incorrectly calculate the loss amount or to confuse the loss percentage with the selling price directly.
Explanations:
To find the selling price after a 15% loss, we first calculate the loss amount:
1. Calculate 15% of the cost price: \( 15\% \times 90 = 0.15 \times 90 = 13.50 \).
2. Subtract the loss amount from the cost price: \( 90 - 13.50 = 76.50 \).
Thus, the selling price is $76.50.
Option Analysis:
Option A:
$ 103.50 is incorrect because it represents a price higher than the cost price, which would indicate a profit, not a loss.
Option B:
$ 80 is incorrect because it does not accurately reflect the 15% loss calculation.
Option C:
75 is incorrect because it does not accurately reflect the 15% loss calculation.
Option D:
$ 76.50 is correct as it accurately reflects the 15% loss calculation.
6.
Jenner is making board games to raise money for a school fundraiser. It costs him $ 40 in materials to make 4 board games. He sells each board game for $ 20. What is his profit on 8 board games?
A) $ 160.
B) $ 20.
C) $ 40.
D) $ 80.
Show Answer
Correct Answer:
Correct answer is: (D) $ 80.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Moderate
Concept notes:
Profit is calculated as the total revenue minus the total cost. In this problem, we need to determine the profit from selling 8 board games.
Common Mistakes:
A common mistake is to calculate the profit per game and then multiply by 8, without considering the total cost for 8 games.
Explanations:
1. Calculate the cost to make 8 board games:
- Cost to make 4 board games = $40
- Cost to make 8 board games = $40 * (8/4) = $80
2. Calculate the revenue from selling 8 board games:
- Selling price per game = $20
- Revenue from 8 games = $20 * 8 = $160
3. Calculate the profit:
- Profit = Revenue - Cost
- Profit = $160 - $80 = $80
Option Analysis:
Option A:
$160 is incorrect because it represents the total revenue, not the profit.
Option B:
$20 is incorrect because it does not account for the total cost of making 8 board games.
Option C:
$40 is incorrect because it does not account for the total revenue and cost for 8 board games.
Option D:
$80 is correct because it represents the profit after subtracting the total cost from the total revenue.
7.
If C.P = Rs 500 and S.P = Rs 600 then there will be
A) Profit 100.
B) Loss 100.
C) Profit 1100.
D) Loss 1100.
Show Answer
Correct Answer:
Correct answer is: (A) Profit 100.
Exam Relevance:
CAT, GMAT, GRE, SAT
Difficulty:
Easy
Concept notes:
Profit is calculated as the difference between the selling price (S.P) and the cost price (C.P) when the S.P is greater than the C.P.
Common Mistakes:
A common mistake is to confuse profit with loss. Profit occurs when the selling price is higher than the cost price, while loss occurs when the selling price is lower than the cost price.
Explanations:
The cost price (C.P) is Rs 500 and the selling price (S.P) is Rs 600. Since the selling price is higher than the cost price, there is a profit. The profit is calculated as follows:
\[ \text{Profit} = \text{S.P} - \text{C.P} = 600 - 500 = 100 \]
Thus, the profit is Rs 100.
Option Analysis:
Option A:
Correct. The profit is Rs 100.
Option B:
Incorrect. There is a profit, not a loss.
Option C:
Incorrect. The profit is Rs 100, not Rs 1100.
Option D:
Incorrect. There is a profit, not a loss.
8.
What was the selling price of the hat that Fred bought for $ 58.75 and sold at a profit of $ 25?
A) $ 33.75.
B) $ 58.75.
C) $ 73.75.
D) $ 83.75.
Show Answer
Correct Answer:
Correct answer is: (D) $ 83.75.
Exam Relevance:
GMAT, GRE, CAT, SAT
Difficulty:
Moderate
Concept notes:
In profit and loss problems, the selling price is calculated by adding the profit to the cost price.
Common Mistakes:
A common mistake is to confuse the cost price with the selling price or to subtract the profit instead of adding it.
Explanations:
The cost price of the hat is $58.75. Fred sold the hat at a profit of $25. Therefore, the selling price is calculated as follows:
\[
\text{Selling Price} = \text{Cost Price} + \text{Profit}
\]
\[
\text{Selling Price} = 58.75 + 25 = 83.75
\]
Thus, the selling price of the hat is $83.75.
Option Analysis:
Option A:
$33.75 is incorrect because it is the result of subtracting the profit from the cost price, not adding it.
Option B:
$58.75 is incorrect because it is the cost price, not the selling price.
Option C:
$73.75 is incorrect because it is not the correct sum of the cost price and profit.
Option D:
$83.75 is correct because it is the sum of the cost price and the profit.
9.
The price at which an article is sold is called .....
A) Cost price.
B) Profit.
C) Loss.
D) Selling price.
Show Answer
Correct Answer:
Correct answer is: (D) Selling price.
Exam Relevance:
CAT, GMAT, GRE, SAT
Difficulty:
Easy
Concept notes:
The price at which an article is sold is known as the selling price.
Common Mistakes:
A common mistake is confusing the selling price with the cost price, which is the price at which an article is purchased.
Explanations:
The selling price is the amount of money received when an article is sold. It is a fundamental concept in profit and loss calculations, as it is used to determine whether a profit or loss has been made.
Option Analysis:
Option A:
Cost price is the price at which an article is purchased, not sold.
Option B:
Profit is the difference between the selling price and the cost price, not the price at which an article is sold.
Option C:
Loss is the difference between the cost price and the selling price when the selling price is less than the cost price, not the price at which an article is sold.
Option D:
Selling price is the price at which an article is sold.
10.
A blender was bought for $ 530.00 and sold for $ 325.00. What was the profit or loss?
A) $ 205.00 profit.
B) $ 205.00 loss.
C) $ 105.00 profit.
D) $ 105.00 loss.
Show Answer
Correct Answer:
Correct answer is: (B) $ 205.00 loss.
Exam Relevance:
GMAT, GRE, SAT, ACT
Difficulty:
Moderate
Concept notes:
Profit or loss is determined by comparing the selling price to the cost price. If the selling price is less than the cost price, a loss is incurred.
Common Mistakes:
A common mistake is to confuse profit with loss. Profit occurs when the selling price is greater than the cost price, while a loss occurs when the selling price is less than the cost price.
Explanations:
The cost price of the blender is $530.00 and the selling price is $325.00. To determine the loss, we subtract the selling price from the cost price:
\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} \]
\[ \text{Loss} = 530.00 - 325.00 \]
\[ \text{Loss} = 205.00 \]
Thus, the loss is $205.00.
Option Analysis:
Option A:
Incorrect, as the selling price is less than the cost price, indicating a loss, not a profit.
Option B:
Correct, as the selling price is less than the cost price, resulting in a loss of $205.00.
Option C:
Incorrect, as the selling price is less than the cost price, indicating a loss, not a profit.
Option D:
Incorrect, as the loss is $205.00, not $105.00.
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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 a product, while the selling price is the amount at which the product is sold to a customer.
How do you calculate profit percentage?
Profit percentage is calculated by dividing the profit by the cost price and then multiplying by 100 to get a percentage.
What is the scope of profit and loss calculations in real-world scenarios?
Profit and loss calculations are essential in business for determining financial performance, making pricing decisions, and assessing the profitability of products or services.
How can understanding cost per unit help in business?
Understanding cost per unit helps businesses set appropriate prices, manage inventory, and identify areas where cost reductions can be made to improve profitability.
What skills are necessary to solve profit and loss problems effectively?
Effective problem-solving in profit and loss requires skills in basic arithmetic, understanding of financial terms, and the ability to apply formulas to real-world situations.