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📝 How to find discount amount (12 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 12 questions available

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What is How to find discount amount?

Definition:
The discount amount is the actual monetary reduction applied to the original price of an item, calculated by multiplying the original price by the discount rate (expressed as a decimal), and it represents how much you save when a discount is offered, with the formula $\text{Discount Amount} = \text{Original Price} \times \text{Discount Rate}$ .

Working:
To find the discount amount, convert the discount percentage to a decimal by dividing by 100, then multiply this decimal by the original price, so if the original price is $P$ and the discount rate is $d\%$ , the discount amount is $\text{Discount Amount} = P \times \frac{d}{100}$ , and this value is subtracted from the original price to get the sale price.

Example:
If a jacket originally costs $\80 \) and is on sale at a 25% discount, then the discount amount is $80 \times 0.25 = \20$ , meaning you save $\$20$ on the jacket.

Reason:
Finding the discount amount is useful for shoppers to understand how much they will save, for businesses to set attractive pricing strategies, and for calculating the final cost of items during sales, promotions, or when negotiating prices.

Easy

Medium

Hard

📝 All How to find discount amount MCQs

Q1. A jacket has a marked price of $\$80$ and is advertised at a $15\%$ discount. What is the amount of the discount?

\$10

\$12

✅

\$13

\$15

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The discount amount is found by multiplying the original price by the discount rate: $80(0.15)=12$ . Therefore, the customer receives a discount of $\$12$ , not the final selling price.

Q2. A store lists a backpack for $\$64$ and applies a $25\%$ discount. Which calculation correctly determines the amount saved?

64\div25

64(25)

64(0.25)

✅

64-0.25

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: A percentage must be converted to decimal form before multiplying by the original price. Since $25\%=0.25$ , the discount is $64(0.25)=16$ . Thus, the amount saved is $\$16$ .

Q3. Two stores sell the same calculator originally priced at $\120 \). Store A offers $20\%$ off, while Store B offers a $\22$ discount. Which store gives the greater discount, and by how much?

A.Store A by

\$2

✅

B.Store B by

\$2

C.Store A by

\$4

D.Both discounts are equal

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Store A's discount is $120(0.20)=24$ dollars, while Store B's discount is $22$ dollars. Comparing the two amounts shows that Store A saves the customer $\$2$ more.

Q4. A student claims that a $30\%$ discount on an item costing $\150 \) means the discount is $\45$ , because $150-30=120$ . What is the correct reasoning?

A.The discount is

\$30

B.The discount is

\$45

✅

C.The discount is

\$120

D.The discount is

\$180

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The student's subtraction treats $30\%$ as $\30 \), which is incorrect. Converting $30\%$ to $0.30$ gives $150(0.30)=45$ . Therefore, the correct discount is $\45$ .

Q5. A retailer gives $12.5\%$ off a table priced at $\240 \). A customer incorrectly calculates the discount as $\30$ by multiplying $240$ by $12.5$ . Which explanation best identifies the error?

A.The price should be divided by

12.5

B.The percentage must be written as

0.125

before multiplication ✅

C.The percentage must be increased to

25\%

D.The discount must be subtracted before finding it

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The calculation uses $12.5$ instead of its decimal equivalent. Since $12.5\%=0.125$ , the correct discount is $240(0.125)=30$ . The numerical answer happens to be obtained only if the conversion is handled properly.

Q6. A bicycle is priced at $\480 \). A coupon reduces the price by $15\%$ , and the store then gives an additional $\20$ promotional reduction. If the question asks only for the percentage discount amount, what should be reported?

\$72

✅

\$92

\$408

\$428

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The percentage discount amount is specifically $15\%$ of the original $\480$ , giving $480(0.15)=72$ . The separate $\20$ promotion changes the total savings but is not part of the percentage discount amount.

Q7. A graph plots discount amount $D$ against original price $P$ for a constant $10\%$ discount. The plotted points are $(100,10)$ , $(200,20)$ , and $(300,30)$ . Based on this relationship, what discount corresponds to $\$450$ ?

\$40

\$45

✅

\$50

\$55

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The graph shows a constant proportional relationship: every $\100 \) of original price produces $\10$ of discount. Therefore, $D=0.10P$ , and for $P=450$ , the discount is $\$45$ .

Q8. A shop offers $35\%$ off a $\$200$ coat. A second shop offers $25\%$ off the same coat followed by another $10\%$ reduction of the already reduced price. Which statement is correct about the first discount amounts?

A.The first shop's discount is

\$20

greater

B.The second shop's combined discount is exactly

35\%

C.The first shop's discount is

\<span class="katex-error" title="ParseError: KaTeX parse error: Can&#x27;t use function &#x27;

' in math mode at position 4: 70 \̲)̲, while the sec…" style="color:#cc0000">70 \), while the second shop's first discount is

\</span>50

✅

D.Both shops initially discount

\$35

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The first shop's discount is $200(0.35)=70$ dollars. The second shop initially discounts $200(0.25)=50$ dollars, then applies another reduction later. Thus, the initial discount amounts are $\70$ and $\50$ , respectively.

Q9. A retailer records these original prices and discount amounts: $\50\rightarrow\5$ , $\100\rightarrow\10$ , $\150\rightarrow\15$ , and $\250\rightarrow\25$ . A student concludes the discount rate must increase as price increases. Which evaluation is best?

A.Correct, because the discount amount increases

B.Incorrect, because the discount rate remains

10\%

✅

C.Correct, because the prices form an arithmetic sequence

D.Incorrect, because the discount rate is

25\%

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Each discount amount is exactly one-tenth of the corresponding original price: $5/50=10/100=15/150=25/250=10\%$ . The dollar discount increases, but the percentage rate remains constant.

Q10. A sports store advertises a $22\%$ discount on equipment priced at $\350 \). The manager wants the discount amount to be at least $\80$ . Does the advertised discount meet the requirement?

A.Yes, by

\$3

B.Yes, by

\$7

C.No, it falls short by

\$3

✅

D.No, it falls short by

\$7

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The discount is $350(0.22)=77$ dollars. Since the required discount is $\$80$ , the promotion falls short by $80-77=3$ dollars. Therefore, the advertised discount does not meet the manager's target.

Q11. An online store offers a $20\%$ discount on an item. The seller wants the discount amount to equal $\$36$ . What original price must the item have, assuming the discount rate applies to the entire original price?

\$160

\$170

\$180

✅

\$200

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Let the original price be $P$ . The discount condition is $0.20P=36$ . Dividing both sides by $0.20$ gives $P=180$ . Thus, an original price of $\180 \) produces exactly a $\36$ discount.

Q12. A store offers a $40\%$ discount on a product. Another store offers a fixed $\$96$ discount on the same product. For what original price would the two discounts be equal, and why?

\$192

, because

0.40(192)=76.80

\$240

, because

0.40(240)=96

✅

\$280

, because

280-96=184

\$384

, because

384\div40=96

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: To make the discounts equal, set $0.40P=96$ . Solving gives $P=96/0.40=240$ . At an original price of $\240 \), the percentage discount and fixed discount both equal $\96$ .

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