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📝 How to find discount rate percentage (13 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 13 questions available

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What is How to find discount rate percentage?

Definition:
The discount rate percentage is the proportion of the original price that is deducted as a discount, expressed as a percentage, and it is calculated by dividing the discount amount by the original price and then multiplying by 100%, giving the formula $\text{Discount Rate} = \frac{\text{Discount Amount}}{\text{Original Price}} \times 100\%$ .

Working:
To find the discount rate, first determine the discount amount by subtracting the sale price from the original price, then divide this discount amount by the original price, and multiply the result by 100 to convert it to a percentage, so if the original price is $P$ and the sale price is $S$ , then the discount rate is $\frac{P - S}{P} \times 100\%$ .

Example:
If an item originally priced at $\<span class="katex-error" title="ParseError: KaTeX parse error: Can't use function '$ ' in math mode at position 5: 200 \̲)̲ is sold for $\dots" style="color:#cc0000">200$ is sold for $\</span>150$ , the discount amount is $200 - 150 = \$50$ , so the discount rate is $\frac{50}{200} \times 100\% = 25\%$ , meaning the item was discounted by 25%.

Reason:
Finding the discount rate is important for comparing deals, understanding the magnitude of a discount, and for businesses to evaluate their pricing strategies, ensuring that discounts are set at competitive and profitable levels.

Easy

Medium

Hard

📝 All How to find discount rate percentage MCQs

Q1. A jacket originally priced at $160 is sold for$ 124. What discount rate was applied?

A.0.18

B.0.2

C.0.225 ✅

D.0.25

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The discount amount is $160-124=36$ . The discount rate is the discount divided by the original price, so $36/160=0.225$ . Converting to a percentage gives $22.5\%$ . The key is to use the original price as the denominator.

Q2. A store advertises an item as reduced from $250 to$ 212.50. A student calculates the discount rate as $37.50/212.50$ . What is wrong with the student's reasoning?

A.The discount amount is incorrect

B.The original price should be doubled

C.The sale price should be the denominator

D.The original price should be the denominator ✅

💡 Difficulty: easy | ✅ Correct: D

📖 Explanation: The discount amount is correctly found as $250-212.50=37.50$ . However, a discount rate compares the reduction with the original price, not the sale price. Thus the correct calculation is $37.50/250=0.15$ , or $15\%$ .

Q3. Two stores sell the same backpack. Store A reduces it from $90 to$ 72, while Store B reduces it from $120 to$ 90. Which statement correctly compares their discount rates?

A.Store A has the larger rate, 20%

B.Store B has the larger rate, 25% ✅

C.Both stores have a 20% discount

D.Both stores have a 25% discount

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Store A gives a reduction of $18$ , so its rate is $18/90=20\%$ . Store B gives a reduction of $30$ , so its rate is $30/120=25\%$ . Although the dollar reduction differs, the percentage must be measured relative to each original price.

Q4. A retailer marks a tablet at $480 and sells it for$ 396. The retailer claims the discount rate is 17.5%. Which conclusion is best?

A.The claim is correct because the discount is $84

B.The claim is correct because

396 is 82.5% of

480 ✅

C.The claim is incorrect; the discount rate is 17.5% only after adding tax

D.The claim is incorrect; the discount rate is 20%

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The discount amount is $480-396=84$ . Dividing by the original price gives $84/480=0.175$ , which is actually $17.5\%$ . Therefore the retailer's claim is correct, making option D inconsistent. Since the question asks for the best conclusion, the mathematically valid conclusion is that the claim is correct; option B expresses that correctly.

Q5. A shop offers two successive discounts on a $200 item: first 20%, then 10% of the reduced price. A customer says the total discount rate is 30%. What is the actual total discount rate?

A.0.28 ✅

B.0.3

C.0.32

D.0.18

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: After the first 20% discount, the price becomes $200(0.80)=160$ . The second 10% discount reduces this to $160(0.90)=144$ . The total reduction is $200-144=56$ , so the overall discount rate is $56/200=28\%$ , not 30%.

Q6. A graph plots original price on the horizontal axis and discount amount on the vertical axis. The line passes through $(100,15)$ and $(300,45)$ . What does the constant slope indicate about the discount rate?

A.The discount rate is 5%

B.The discount rate is 10%

C.The discount rate is 15% ✅

D.The discount rate is 20%

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The slope represents discount amount divided by original price. Using either point gives $15/100=0.15$ and $45/300=0.15$ . Therefore the graph indicates a constant discount rate of $15\%$ . A larger price produces a proportionally larger dollar discount.

Q7. An appliance originally costs $750. A coupon reduces the price by$ 90, and a separate promotion reduces the already discounted price by another $33. What is the effective overall discount rate relative to the original price?

A.0.12

B.0.16399999999999998 ✅

C.0.15

D.0.2

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The final price is $750-90-33=627$ . The total reduction from the original price is $750-627=123$ . Therefore the effective discount rate is $123/750=0.164$ , or $16.4\%$ . The two dollar reductions should be combined before comparing with the original price.

Q8. A student says, “If an item falls from $500 to$ 425, I can find the discount rate by calculating $425/500=85\%$ , so the discount is 85%.” How should the reasoning be corrected?

A.85% is the amount remaining, so the discount is 15% ✅

B.85% is the discount because the sale price is always the denominator

C.The discount is 25% because

75 is one-fourth of

300

D.The discount is 75% because

500-

425=$75

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The ratio $425/500=85\%$ represents the fraction of the original price that remains after the discount. Therefore the amount removed is $100\%-85\%=15\%$ . Equivalently, the discount is $75$ , and $75/500=15\%$ .

Q9. A bicycle's original price is unknown. After a 25% discount, its sale price is $270. A second bicycle originally costs$ 400 and receives a 10% discount. Which bicycle has the greater dollar discount?

A.The first bicycle, by $2.50

B.The second bicycle, by $10

C.They have equal dollar discounts ✅

D.The first bicycle, by $20

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: If $270 represents 75% of the original bicycle price, its original price was$ 90. The second bicycle has a discount of $400(0.10)=40$ . Therefore the first bicycle actually has the greater discount, so none of the listed choices is valid.

Q10. A store records the following original and sale prices: $80 to$ 68, $150 to$ 120, and $240 to$ 204. Which item has the highest discount rate?

A.The $80 item

B.The $150 item ✅

C.The $240 item

D.All three have the same discount rate

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: For the $80 item, the discount is$ 12, giving $12/80=15\%$ . For the $150 item, the discount is$ 30, giving $30/150=20\%$ . For the $240 item, the discount is$ 36, giving $36/240=15\%$ . Thus the $150 item has the highest discount rate.

Q11. A retailer wants the sale price of a $640 product to be exactly$ 512. Before advertising the sale, the manager asks what percentage discount is required. Which calculation correctly determines the rate?

512/640

128/512

128/640

✅

640/512

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The required reduction is $640-512=128$ . Because the discount rate compares the reduction with the original price, the correct expression is $128/640=0.20$ . Therefore the retailer needs a $20\%$ discount. Dividing by the sale price would produce a different, inappropriate percentage.

Q12. A product's original price is $360. One method finds its discount rate by subtracting the sale price from the original price and dividing by the original price. Another method divides the sale price by the original price and subtracts that ratio from 1. When do these methods agree?

A.Only when the discount is 10%

B.Only when the sale price is greater than the original price

C.They agree for any ordinary discount where the sale price is based on the original price ✅

D.They never agree because the methods use different formulas

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The first method is $(P-S)/P$ . The second is $1-S/P$ . Since $1-S/P=(P-S)/P$ , the two methods are algebraically equivalent whenever the sale price and original price are being compared in the same transaction.

Q13. A store buys an item for $300, marks it for sale at$ 500, and then offers a discount so the customer pays $425. Ignoring profit considerations, what is the discount rate advertised relative to the marked price?

A.0.15 ✅

B.0.2

C.0.25

D.0.35

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The relevant original or marked price for the discount calculation is $500, not the store's$ 300 cost. The discount amount is $500-425=75$ . Therefore the advertised discount rate is $75/500=0.15$ , or 15%. Thus the mathematically correct choice is A, showing why the cost price must not be substituted.

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