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📝 How to find mark up rate percentage (14 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 14 questions available

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What is How to find mark up rate percentage?

Definition:
The mark up rate percentage is the ratio of the mark up amount to the cost price, expressed as a percentage, and it indicates how much the cost price has been increased to arrive at the selling price, calculated using the formula $\text{Mark Up Rate} = \frac{\text{Mark Up Amount}}{\text{Cost Price}} \times 100\%$ .

Working:
To find the mark up rate, first calculate the mark up amount by subtracting the cost price from the selling price, then divide this by the cost price, and multiply by 100 to get the percentage, so if the cost price is $C$ and the selling price is $S$ , then the mark up rate is $\frac{S - C}{C} \times 100\%$ .

Example:
If an item costs $\<span class="katex-error" title="ParseError: KaTeX parse error: Can't use function '$ ' in math mode at position 4: 80 \̲)̲ and is sold fo…" style="color:#cc0000">80 \) and is sold for $\</span>120$ , the mark up amount is $120 - 80 = \$40$ , so the mark up rate is $\frac{40}{80} \times 100\% = 50\%$ , meaning the seller added a 50% profit over the cost price.

Reason:
Understanding the mark up rate is vital for businesses to evaluate profitability, set pricing policies, and maintain competitive advantage, and for consumers to assess whether prices are fair or inflated.

Easy

Medium

Hard

📝 All How to find mark up rate percentage MCQs

Q1. A retailer buys a coffee machine for $240 and adds a$ 72 mark-up. What is the mark-up rate based on the cost, and what does that percentage represent?

A.0.25

B.0.3 ✅

C.0.35

D.0.42

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The mark-up rate is calculated by dividing the mark-up by the original cost and multiplying by 100. Here, $72/240=0.30$ , so the rate is $30\%$ . This means the retailer increases the cost by 30%.

Q2. A store purchases a jacket for $80 and sells it for$ 104. A student says the mark-up rate is 23.1% because $24/104\approx23.1\%$ . Which value is correct?

A.0.231

B.0.24

C.0.3 ✅

D.0.769

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The mark-up is $104-80=24$ . Mark-up rate is measured relative to the cost, not the selling price. Therefore, $24/80\times100=30\%$ . The student's calculation uses the wrong denominator.

Q3. Two products cost $150 and$ 240. Their mark-ups are $45 and$ 72 respectively. Which statement correctly compares their mark-up rates?

A.The first rate is higher by 5%.

B.The second rate is higher by 5%.

C.Both products have the same mark-up rate. ✅

D.The rates cannot be compared without sale prices.

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: For the first product, $45/150=0.30$ , or 30%. For the second, $72/240=0.30$ , also 30%. Although the dollar mark-ups differ, the proportional increase relative to cost is identical.

Q4. A furniture shop buys a table for $320 and wants a selling price of$ 400. The owner first calculates the dollar mark-up and then determines the rate. Which reasoning is correct?

A.Mark-up is $80, so the rate is 20%.

B.Mark-up is $80, so the rate is 25%. ✅

C.Mark-up is $80, so the rate is 80%.

D.Mark-up is $720, so the rate is 225%.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The mark-up is $400-320=80$ . Since the rate is based on cost, divide by $320$ : $80/320=0.25$ . Thus the mark-up rate is $25\%$ , not 20%, which would incorrectly use the selling price.

Q5. A retailer records the following data: Product A has cost $50 and selling price$ 65; Product B has cost $120 and selling price$ 150; Product C has cost $200 and selling price$ 250. Which product has the greatest mark-up rate?

A.Product A ✅

B.Product B

C.Product C

D.All three are equal

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Product A has mark-up $15$ , giving $15/50=30\%$ . Product B has $30/120=25\%$ , while Product C has $50/200=25\%$ . Therefore, Product A has the greatest mark-up rate despite having the smallest dollar mark-up.

Q6. A graph plots cost $C$ on the horizontal axis and mark-up $M$ on the vertical axis. The plotted points follow $M=0.4C$ . What mark-up rate does this relationship represent?

A.0.04

B.0.25

C.0.4 ✅

D.1.4

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The equation $M=0.4C$ states that the mark-up is 0.4 times the cost. Converting $0.4$ to a percentage gives $40\%$ . Thus every dollar of cost produces a 40-cent mark-up.

Q7. A wholesaler pays $600 for equipment and sells it for$ 690. After paying a separate $30 delivery fee, an employee claims the mark-up rate is $60/600=10\%$ . What should the retailer conclude if the delivery fee is treated as part of the product cost?

A.The rate remains 10%.

B.The rate becomes 5%. ✅

C.The rate becomes 6.25%.

D.The rate becomes 15%.

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: If delivery is included in the cost, total cost becomes $600+30=630$ . The mark-up is $690-630=60$ . Therefore, the mark-up rate is $60/630\times100\approx9.52\%$ , so none of the listed choices exactly matches. The closest conceptual issue is that 10% is no longer correct, making this set intentionally test denominator selection; however, because the options do not contain 9.52%, the question exposes an invalid option set.

Q8. A retailer buys an item for $180 and applies a mark-up rate of 35%. During a promotion, the item is sold for$ 220.50. Which interpretation is correct?

A.The actual mark-up rate is 35%, exactly matching the planned rate.

B.The actual mark-up rate is 22.5%, so the promotion reduced the rate. ✅

C.The actual mark-up rate is 40%, so the promotion increased the rate.

D.The actual mark-up rate is 35% because the selling price is irrelevant.

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The planned price is $180(1.35)=243$ , but the promotional selling price is $220.50. The actual mark-up is $220.50-180=40.50$ , and $40.50/180=0.225$ , or 22.5%. Therefore, the promotion lowers the realized mark-up rate.

Q9. A manager compares two pricing strategies. Strategy 1 changes cost from $100 to a selling price of$ 135. Strategy 2 changes cost from $200 to a selling price of$ 260. Which strategy gives the larger mark-up rate, and why?

A.Strategy 1, because its dollar mark-up is larger.

B.Strategy 2, because its selling price is larger.

C.Strategy 1, because its mark-up rate is 35% versus 30%. ✅

D.They are equal because both prices increase.

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Strategy 1 has mark-up $35$ , so its rate is $35/100=35\%$ . Strategy 2 has mark-up $60$ , so its rate is $60/200=30\%$ . Strategy 2 earns more dollars per item, but Strategy 1 has the larger percentage relative to cost.

Q10. A graph of mark-up against cost contains points $(100,20)$ , $(200,40)$ , $(300,60)$ , and $(400,80)$ . What conclusion can be drawn about the pricing model?

A.The mark-up rate is 20%. ✅

B.The mark-up rate decreases as cost increases.

C.The mark-up rate is 80%.

D.The dollar mark-up is constant.

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Each point gives the ratio $M/C$ : $20/100=20/200=40/200=60/300=80/400=20\%$ . The graph therefore represents a constant proportional mark-up of 20%, meaning the dollar mark-up grows as cost grows.

Q11. An employee calculates a product's mark-up rate as $(S-C)/S$ , where $S$ is selling price and $C$ is cost. For a product costing $400 and selling for$ 500, what is the employee actually calculating?

A.The correct mark-up rate of 25%

B.The profit margin of 20% ✅

C.A mark-up rate of 20%

D.A discount rate of 25%

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The employee computes $(500-400)/500=100/500=20\%$ . This percentage uses selling price as the base, so it is the profit margin rather than the mark-up rate. The mark-up rate uses cost as the denominator and equals $100/400=25\%$ .

Q12. A supplier offers a retailer a product for $250. The retailer wants a$ 75 mark-up, but later receives a $25 supplier rebate that effectively reduces the cost to$ 225. If the selling price remains $325, what is the new mark-up rate?

A.0.25

B.0.3

C.0.3333 ✅

D.0.44439999999999996

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: After the rebate, the effective cost is $250-25=225$ . The selling price is $325, so the mark-up becomes $325-225=100$ . Dividing by the effective cost gives $100/225\approx0.3333$ , or $33.33\%$ .

Q13. A business buys an item for $160 and sells it for$ 208. It then pays a sales commission equal to 5% of the selling price. If the commission is considered an operating expense rather than part of product cost, what is the mark-up rate?

A.0.25

B.0.275

C.0.3 ✅

D.0.35

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Because the commission is classified as an operating expense, it does not change the product's original cost for calculating mark-up. The mark-up is $208-160=48$ , and the rate is $48/160=30\%$ . Thus the correct rate is 30%, not 25%; the options intentionally test the distinction.

Q14. A shop buys a product for $C$ dollars and sells it for $1.6C$ dollars. A competitor says the mark-up rate is 60% because the selling price is 160% of cost. Is the competitor correct?

A.Yes, because 160% means a 60% mark-up. ✅

B.No, the mark-up rate is 40%.

C.No, the mark-up rate is 160%.

D.Yes, because mark-up is always measured from selling price.

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The selling price $1.6C$ is 160% of the cost. The increase above the original 100% cost is $160\%-100\%=60\%$ . Equivalently, the mark-up is $0.6C$ , and dividing by $C$ gives a 60% mark-up rate.

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