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📝 How to find original list price from mark up (11 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 11 questions available

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What is How to find original list price from mark up?

Definition:
The original list price (or selling price) is the price at which an item is offered for sale after a mark up has been applied to the cost price, and it can be found by adding the mark up amount to the cost price, or if the mark up rate is known, by multiplying the cost price by $1 + \text{mark up rate}$ , giving $\text{Selling Price} = \text{Cost Price} \times (1 + \text{Mark Up Rate})$ .

Working:
To find the original list price from the mark up, first ensure the mark up rate is in decimal form, then multiply the cost price by the factor $1 + r$ , where $r$ is the mark up rate, so if the cost is $C$ and the mark up rate is $r$ , the selling price is $S = C \times (1 + r)$ , and this gives the list price before any discounts.

Example:
If a store buys a product for $\<span class="katex-error" title="ParseError: KaTeX parse error: Can't use function '$ ' in math mode at position 4: 50 \̲)̲ and wants a ma…" style="color:#cc0000">50 \) and wants a mark up rate of 40%, the selling price is $50 \times (1 + 0.40) = 50 \times 1.40 = \</span>70$ , so the original list price is $\$70$ .

Reason:
Finding the original list price from the mark up is crucial for retailers to set appropriate pricing that ensures profitability, for wholesalers to determine selling prices, and for comparing prices across different suppliers or market conditions.

4

Easy

4

Medium

3

Hard

📝 All How to find original list price from mark up MCQs

Q1. A store marks up an item by 25% of its cost. If the cost is $80, which expression correctly represents the item's list price before any discount?</p><div class="options-grid"><div class="opt-item "><span class="label">A.</span><span class="text">$ 80+25

B.-801.25 ✅

C.-800.25

D.$80÷1.25

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: A 25% mark-up means the increase is 25% of the original cost, not a fixed $25. The mark-up is 0.25(80)=20, so the list price is 80+20=100, represented by 80(1.25).

Q2. A retailer calculates a 40% mark-up on an item's cost. Which statement best explains why dividing the cost by 0.60 would not correctly find the list price?

A.It would calculate a 40% increase

B.It treats the mark-up as 60% of the cost

C.It assumes the cost is 60% of the list price ✅

D.It subtracts the mark-up twice

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: With a 40% mark-up, the list price is 140% of cost, so $L=1.40C$ . Dividing by 0.60 instead assumes the original cost represents 60% of the list price, which is a different percentage relationship.

Q3. A wholesaler pays $150 for a device and applies a 32% mark-up. The store then wants a list price that is a whole dollar amount. What should the list price be?

A.182

B.192

C.198 ✅

D.200

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The mark-up is 0.32(150)=48. Adding this to the original cost gives 150+48=198. Therefore, the correct list price is $198, and the whole-dollar requirement does not change the calculation.

Q4. A furniture shop buys a table for $240. It wants a 35% mark-up based on cost, but first adds a fixed$ 12 handling expense to the amount used for pricing. What list price results?

A.324

B.331.2

C.340.2 ✅

D.352.8

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The pricing base becomes $240+12=252$ because the handling expense is included before applying the mark-up. A 35% mark-up is 0.35(252)=88.20, giving a list price of $252+88.20=340.20$ .

Q5. Two employees calculate the list price of an item costing $500 with a 30% mark-up. Employee A gets$ 650 by adding 30% of cost. Employee B gets $714.29 by dividing by 0.70. Who is correct?

A.Only Employee A, because mark-up is based on cost ✅

B.Only Employee B, because list price must exceed cost

C.Both are correct because the methods are equivalent

D.Neither is correct because the mark-up should be $300

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: When the mark-up is based on cost, the list price is $C(1+r)$ . Thus $500(1.30)=650$ . Dividing by 0.70 would represent a situation where cost is 70% of list price, which is a different pricing assumption.

Q6. A product has a cost of $320 and a list price of$ 416. A student claims the mark-up rate is 30% because $416-320=96$ and $96\div320$ is approximately 0.30. What is the actual mark-up rate?

A.0.2

B.0.25

C.0.3 ✅

D.0.35

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The difference between list price and cost is $416-320=96$ . Dividing by the original cost gives $96/320=0.30$ , or 30%. The student is correct because mark-up rate is measured relative to cost in this situation.

Q7. A shop's pricing model is $L=C(1+r)$ . If the cost increases from $200 to$ 250 while the mark-up rate remains 20%, how much does the list price increase?

A.50

B.60 ✅

C.70

D.100

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The original list price is $200(1.20)=240$ . The new list price is $250(1.20)=300$ . Therefore, the list price increases by $300-240=60$ . The percentage mark-up stays fixed, so the absolute increase grows with cost.

Q8. A retailer records the following cost-to-list-price pattern: a cost of $100 corresponds to$ 125, $200 corresponds to$ 250, and $300 corresponds to$ 375. Based on this pattern, what list price corresponds to a cost of $440?

A.500

B.525

C.550 ✅

D.575

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Each listed price is 1.25 times its cost: $125/100=250/200=375/300=1.25$ . Applying the same proportional relationship gives $440(1.25)=550$ . Therefore, the predicted list price is $550.

Q9. A graph of list price $L$ versus cost $C$ is a straight line through $(0,0)$ and $(200,260)$ . If the same relationship continues, which list price corresponds to a cost of $350?

A.390

B.420

C.455 ✅

D.520

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The graph indicates a proportional relationship because the line passes through the origin. Its ratio is $260/200=1.30$ , meaning $L=1.30C$ . For $C=350$ , the list price is $1.30(350)=455$ .

Q10. A store wants its list price to be $468 after applying a 30% mark-up to cost. A salesperson says the cost must be$ 327.60 because they subtract 30% from $468. Which value is the correct cost?

A.327.6

B.360 ✅

C.374.4

D.390

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: A 30% mark-up means $L=1.30C$ , so the cost must be found by $C=468/1.30=360$ . Simply subtracting 30% from the final price is incorrect because the 30% is calculated from cost, not from list price.

Q11. A company uses two possible pricing methods for a product costing $400. Method A applies a 45% mark-up to cost. Method B sets the list price so that the cost represents 55% of the list price. Which method produces the higher list price?</p><div class="options-grid"><div class="opt-item "><span class="label">A.</span><span class="text">Method A, by$ 18.18

B.Method B, by $18.18 ✅

C.They produce the same list price

D.Method A, by $36.36

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: Method A gives $400(1.45)=580$ . Method B requires $400=0.55L$ , so $L=400/0.55\approx727.27$ . Therefore Method B is higher by approximately $727.27-580=147.27$ , making the percentage-base distinction crucial.

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