This quiz works best with JavaScript enabled.
Home
>
Unit V Mathematical Reasoning And Aptitude
>
Percentage Applications – Quiz 15
Percentage Applications Quiz 15 (10 MCQs)
This quiz evaluates understanding of discount calculation, tax application, total cost, VAT calculation, and percentage applications. It assesses skills in solving for original price, expenditure adjustment, quantity reduction, loss calculation, financial mathematics, and rounding percentages. Concepts include price reduction, income tax, reverse percentage calculation, and price determination.
Quiz Instructions
Select an option to see the correct answer instantly.
1.
If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
A) 10%.
B) 12%.
C) 8%.
D) 7%.
Show Answer
Correct Answer:
Correct answer is: (C) 8%.
Exam Relevance:
CAT, GMAT, GRE, SAT
Difficulty:
Moderate
Concept notes:
The problem involves understanding how changes in price and expenditure affect the quantity purchased. The key is to use the concept of percentage change and its application in real-world scenarios.
Common Mistakes:
A common mistake is to assume that the percentage reduction in quantity purchased is directly proportional to the percentage increase in price, without considering the additional expenditure Raj is willing to incur.
Explanations:
Let the original price of petrol be \( P \) and the original quantity purchased be \( Q \). The original expenditure is \( P \times Q \).
After a 25% increase in price, the new price is \( 1.25P \). Raj intends to spend only an additional 15% on petrol, so the new expenditure is \( 1.15 \times (P \times Q) \).
Let the new quantity purchased be \( Q' \). The new expenditure can also be expressed as \( 1.25P \times Q' \).
Equating the two expressions for the new expenditure:
\[ 1.25P \times Q' = 1.15 \times (P \times Q) \]
Solving for \( Q' \):
\[ Q' = \frac{1.15 \times (P \times Q)}{1.25P} \]
\[ Q' = \frac{1.15}{1.25} \times Q \]
\[ Q' = 0.92 \times Q \]
The reduction in quantity purchased is:
\[ Q - Q' = Q - 0.92Q = 0.08Q \]
Thus, the percentage reduction in quantity purchased is:
\[ \frac{0.08Q}{Q} \times 100\% = 8\% \]
Option Analysis:
Option A:
10% is incorrect because it does not account for the additional 15% expenditure Raj is willing to incur.
Option B:
12% is incorrect because it overestimates the reduction in quantity purchased.
Option C:
8% is correct as calculated above.
Option D:
7% is incorrect because it underestimates the reduction in quantity purchased.
2.
A store increases the price of a $ 50 item by 10%. What is the new price?
A) $ 55.
B) $ 60.
C) $ 50.
D) $ 45.
Show Answer
Correct Answer:
Correct answer is: (A) $ 55.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The concept involves calculating a percentage increase and adding it to the original price.
Common Mistakes:
A common mistake is to add the percentage directly to the original price without converting it to a decimal first.
Explanations:
To find the new price after a 10% increase, first calculate 10% of $50.
10% of $50 is calculated as \( \frac{10}{100} \times 50 = 5 \).
Adding this to the original price: \( 50 + 5 = 55 \).
Thus, the new price is $55.
Option Analysis:
Option A:
Correct. The new price after a 10% increase is $55.
Option B:
Incorrect. This would be the price if the increase was 20%.
Option C:
Incorrect. This is the original price, not the increased price.
Option D:
Incorrect. This would be the price if there was a 10% decrease.
3.
Emma, Lily, and Scarlett are on a shopping spree! Emma found a cute dress that costs $ 100. If she gets a 30% discount, how much will she save?
A) $ 30.
B) $ 70.
C) $ 20.
D) $ 40Tags6.NS.B.
Show Answer
Correct Answer:
Correct answer is: (A) $ 30.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Easy
Concept notes:
The concept of percentage applications involves calculating the amount saved or discounted based on a given percentage.
Common Mistakes:
A common mistake is to calculate the final price after the discount instead of the amount saved.
Explanations:
To find the amount saved, we need to calculate 30% of the original price of the dress. The original price is $100.
Step 1: Convert the percentage to a decimal.
30% = 0.30
Step 2: Multiply the original price by the decimal.
$100 × 0.30 = $30
Therefore, Emma will save $30 with the 30% discount.
Option Analysis:
Option A:
Correct. The amount saved is $30.
Option B:
Incorrect. This is the price after the discount, not the amount saved.
Option C:
Incorrect. This is not the correct amount saved.
Option D:
Incorrect. This is not the correct amount saved.
4.
A man's taxable income is $ 35 200. He pays income tax at the rate of 25%. The amount of income tax payable is
A) $ 8000.
B) $ 8800.
C) $ 9200.
D) $ 26400.
Show Answer
Correct Answer:
Correct answer is: (B) $ 8800.
Exam Relevance:
SAT, GRE, GMAT, CPA
Difficulty:
Moderate
Concept notes:
The concept involves calculating the amount of income tax payable based on a given taxable income and tax rate.
Common Mistakes:
A common mistake is to misinterpret the tax rate or taxable income, leading to incorrect calculations.
Explanations:
To find the amount of income tax payable, we use the formula:
\[ \text{Income Tax} = \text{Taxable Income} \times \text{Tax Rate} \]
Given:
- Taxable Income = $35,200
- Tax Rate = 25% (or 0.25 in decimal form)
Step-by-step calculation:
1. Convert the tax rate to a decimal: 25% = 0.25
2. Multiply the taxable income by the tax rate:
\[ 35,200 \times 0.25 = 8,800 \]
Thus, the amount of income tax payable is $8,800.
Option Analysis:
Option A:
$8,000 is incorrect because it does not match the calculated amount.
Option B:
$8,800 is the correct amount of income tax payable.
Option C:
$9,200 is incorrect because it does not match the calculated amount.
Option D:
$26,400 is incorrect because it does not match the calculated amount.
5.
A jacket has a regular price of $ 50. It is on sale for 20% off. The sales tax is 7%. What is the total cost of the jacket including tax?
A) $ 40.
B) $ 3.50.
C) $ 53.50.
D) $ 42.80.
Show Answer
Correct Answer:
Correct answer is: (D) $ 42.80.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The problem involves calculating the sale price of an item after a discount and then applying sales tax to the discounted price.
Common Mistakes:
A common mistake is to apply the sales tax to the original price instead of the discounted price.
Explanations:
1. Calculate the discount amount: 20% of $50 = 0.20 * $50 = $10.
2. Subtract the discount from the original price: $50 - $10 = $40.
3. Calculate the sales tax on the discounted price: 7% of $40 = 0.07 * $40 = $2.80.
4. Add the sales tax to the discounted price: $40 + $2.80 = $42.80.
Option Analysis:
Option A:
$40 is the price after the discount but before tax.
Option B:
$3.50 is the incorrect tax amount if applied to the original price.
Option C:
$53.50 is the incorrect total if the tax is applied to the original price.
Option D:
$42.80 is the correct total cost after discount and tax.
Mnemonic:
Discount first, then tax.
6.
During a sale, a shopkeeper reduced the prices of all his goods by 10%.Calculate the usual selling price of a saucepan which was sold for $ 24.30 in the sale.
A) $ 26.73.
B) $ 21.87.
C) $ 27.
D) None of above.
Show Answer
Correct Answer:
Correct answer is: (C) $ 27.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The problem involves calculating the original price of an item after a percentage discount has been applied. The key concept is understanding how to reverse the percentage reduction to find the original price.
Common Mistakes:
A common mistake is to incorrectly apply the percentage increase to the sale price, rather than reversing the discount to find the original price.
Explanations:
Let the original price of the saucepan be \( P \).
The saucepan was sold for $24.30 after a 10% discount. This means the sale price is 90% of the original price.
We can set up the equation:
\[ 0.90 \times P = 24.30 \]
To find \( P \), we divide both sides by 0.90:
\[ P = \frac{24.30}{0.90} \]
Perform the division:
\[ P = 27 \]
Thus, the original price of the saucepan is $27.
Option Analysis:
Option A:
$ 26.73 is incorrect because it does not match the calculation of reversing the 10% discount.
Option B:
$ 21.87 is incorrect because it does not match the calculation of reversing the 10% discount.
Option C:
$ 27 is correct because it matches the calculation of reversing the 10% discount.
Option D:
None of the above is incorrect because $27 is the correct answer.
7.
The game system originally cost $ 350. It was on sale for $ 311. Find the percent of decrease. Round to the nearest percent.
A) 13% decrease.
B) 89% decrease.
C) 11% decrease.
D) 113% decrease.
Show Answer
Correct Answer:
Correct answer is: (C) 11% decrease.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The concept of percentage decrease involves calculating the difference between the original and sale prices, then expressing this difference as a percentage of the original price.
Common Mistakes:
A common mistake is to calculate the percentage decrease incorrectly by using the sale price as the base instead of the original price.
Explanations:
To find the percent decrease, follow these steps:
1. Calculate the decrease in price: $350 - $311 = $39.
2. Divide the decrease by the original price: $39 / $350 = 0.1114.
3. Convert the decimal to a percentage: 0.1114 * 100 = 11.14%.
4. Round to the nearest percent: 11.14% ≈ 11%.
Thus, the percent decrease is 11%.
Option Analysis:
Option A:
13% decrease is incorrect because the calculation shows a decrease of 11.14%, which rounds to 11%.
Option B:
89% decrease is incorrect because the decrease is much smaller than 89%.
Option C:
11% decrease is correct as calculated.
Option D:
113% decrease is incorrect because the decrease cannot be more than 100%.
8.
You received your assessment back and you scored 45 points, which was an 80%. How many points was the test out of? Round to the nearest whole point.
A) 36 points.
B) 50 points.
C) 56 points.
D) None of above.
Show Answer
Correct Answer:
Correct answer is: (C) 56 points.
Exam Relevance:
SAT, ACT, GRE, GMAT
Difficulty:
Moderate
Concept notes:
The concept involves understanding how percentages relate to the total score of a test. If a score represents a certain percentage of the total points, we can use the percentage formula to find the total points.
Common Mistakes:
A common mistake is to misinterpret the percentage as a direct ratio without converting it to a decimal or fraction for calculation.
Explanations:
To find the total points of the test, we use the formula:
\[ \text{Total Points} = \frac{\text{Score}}{\text{Percentage}} \times 100 \]
Given:
- Score = 45 points
- Percentage = 80%
First, convert the percentage to a decimal:
\[ 80\% = 0.80 \]
Now, use the formula:
\[ \text{Total Points} = \frac{45}{0.80} \]
Perform the division:
\[ \text{Total Points} = 56.25 \]
Rounding to the nearest whole point:
\[ \text{Total Points} = 56 \]
Thus, the test was out of 56 points.
Option Analysis:
Option A:
36 points is incorrect because it does not satisfy the given percentage and score relationship.
Option B:
50 points is incorrect because it does not satisfy the given percentage and score relationship.
Option C:
56 points is correct as it satisfies the given percentage and score relationship.
Option D:
None of the above is incorrect because 56 points is a valid option.
9.
A book costs $ 30 and is sold for $ 24. What is the loss percentage?
A) 20%.
B) 25%.
C) 15%.
D) 10%.
Show Answer
Correct Answer:
Correct answer is: (A) 20%.
Exam Relevance:
SAT, GRE, GMAT, CAT
Difficulty:
Moderate
Concept notes:
The loss percentage is calculated by finding the difference between the cost price and the selling price, then dividing by the cost price and multiplying by 100.
Common Mistakes:
A common mistake is to calculate the loss percentage based on the selling price instead of the cost price.
Explanations:
1. Calculate the loss: Cost Price (CP) - Selling Price (SP) = $30 - $24 = $6.
2. Calculate the loss percentage: (Loss / Cost Price) * 100 = ($6 / $30) * 100 = 20%.
Option Analysis:
Option A:
Correct. The loss percentage is 20%.
Option B:
Incorrect. 25% is not the correct loss percentage.
Option C:
Incorrect. 15% is not the correct loss percentage.
Option D:
Incorrect. 10% is not the correct loss percentage.
10.
Mansi bought a watch for Rs 1980 including VAT at 10%. Find the original price of the watch.
A) Rs.590.
B) Rs.1800.
C) Rs.1250.
D) Rs.321.
Show Answer
Correct Answer:
Correct answer is: (B) Rs.1800.
Exam Relevance:
CAT, GMAT, GRE, SAT
Difficulty:
Moderate
Concept notes:
The question involves calculating the original price of an item given the final price including VAT. The concept of percentage applications is used to find the original price before the VAT was added.
Common Mistakes:
A common mistake is to assume that the final price is the original price plus 10% of the original price, without correctly accounting for the fact that the final price includes the original price plus the VAT.
Explanations:
Let the original price of the watch be \( P \).
The final price including VAT is given as Rs. 1980, and the VAT rate is 10%.
The final price can be expressed as:
\[ \text{Final Price} = P + 0.10P = 1.10P \]
Given that the final price is Rs. 1980, we can set up the equation:
\[ 1.10P = 1980 \]
To find the original price \( P \), we solve for \( P \):
\[ P = \frac{1980}{1.10} \]
\[ P = 1800 \]
Thus, the original price of the watch is Rs. 1800.
Option Analysis:
Option A:
Rs.590. This is incorrect because it does not account for the 10% VAT correctly.
Option B:
Rs.1800. This is the correct answer as calculated above.
Option C:
Rs.1250. This is incorrect because it does not account for the 10% VAT correctly.
Option D:
Rs.321. This is incorrect because it does not account for the 10% VAT correctly.
← Previous
Next →
Related Quizzes
Frequently Asked Questions
What is the purpose of learning percentage applications?
Learning percentage applications helps in understanding how percentages are used in real-life scenarios such as calculating discounts, tax, and interest rates.
How do you calculate the amount saved with a discount?
To calculate the amount saved with a discount, multiply the original price by the discount percentage and then divide by 100.
What is the difference between percentage increase and percentage decrease?
Percentage increase refers to the growth in a quantity, while percentage decrease refers to the reduction in a quantity, both expressed as a percentage of the original value.
How can you calculate the selling price after a discount?
To calculate the selling price after a discount, subtract the discount amount from the original price.
What is reverse percentage calculation?
Reverse percentage calculation is used to find the original amount when you know the final amount and the percentage change.