Profit and Loss Quiz (Set 2) | Concept of Maths Ranchi

Question 1

1. A manufacturer marks an article $40\%$ above the cost price and allows two successive discounts of $10\%$ and $5\%$ to a retailer. What is the net profit percentage for the manufacturer?

A) $25\%$

B) $20.5\%$

C) $19.7\%$

D) $18.2\%$

Answer

Correct Answer: C

Solution: Let Cost Price ($\text{CP}$) = $100$. Marked Price ($\text{MP}$) = $100 + 40\% \text{ of } 100 = 140$. First discount stage: $140 - (10\% \text{ of } 140) = 140 - 14 = 126$. Second discount stage: $126 - (5\% \text{ of } 126) = 126 - 6.3 = 119.7$. Net Selling Price ($\text{SP}$) = $119.7$. $$\text{Net Profit Percentage} = \text{SP} - \text{CP} = 119.7 - 100 = 19.7\%.$$

Question 2

2. A dishonest shopkeeper claims to sell his goods at a loss of $4\%$, but he uses a weight of $900$ grams instead of $1\text{ kg}$. What is his actual profit percentage?

A) $6.25\%$

B) $6.66\%$

C) $7.14\%$

D) $5.55\%$

Answer

Correct Answer: B

Solution: Let the true $\text{CP}$ of $1000\text{g}$ be $1000\text{ units}$. Claimed selling profile $\text{SP} = 1000 - 4\% = 960\text{ units}$. Actual physical quantity delivered = $900\text{g}$. Effective cost of this quantity = $900\text{ units}$. $$\text{Absolute Profit Amount} = \text{SP} - \text{Actual CP} = 960 - 900 = 60\text; units.$$ $$\text{Real Profit Percentage} = \left(\frac{60}{900}\right) \times 100 = \frac{100}{15} \approx 6.66\%.$$

Question 3

3. If a merchant estimates his profit as $20\%$ of the selling price, what is his actual profit percentage calculated on the cost price?

Question 4

4. A sold an item to B at a gain of $20\%$. B sold it to C at a loss of $10\%$. If C paid $\$1080$ for it, at what price did A purchase the item?

A) $\$1000$

B) $\$950$

C) $\$1100$

D) $\$1050$

Answer

Correct Answer: A

Solution: Let A's purchasing cost ($\text{CP}$) be $x$. B's acquisition price = $x \times 1.20$. C's final purchase price = $(x \times 1.20) \times 0.90 = 1.08x$. Given that $1.08x = 1080$: $$x = \frac{1080}{1.08} = 1000.$$ A purchased the item for **$\$1000$**.

Question 5

5. By selling $45$ lemons for $\$40$, a man loses $20\%$. How many lemons should he sell for $\$24$ to gain $20\%$ in the transaction?

A) $15$

B) $20$

C) $18$

D) $22$

Answer

Correct Answer: C

Solution: $\text{SP}$ of $45$ lemons = $\$40 \implies \text{SP}$ of $1$ lemon = $\frac{40}{45} = \frac{8}{9}$. Since this transaction hits a $20\%$ loss, $\text{CP}$ of $1$ lemon = $\frac{8/9}{0.80} = \frac{8}{9} \times \frac{5}{4} = \frac{10}{9}$. To target a clean $20\%$ gain, target $\text{SP} of 1 lemon = \frac{10}{9} \times 1.20 = \frac{10}{9} \times \frac{6}{5} = \frac{4}{3}$. $$\text{Target Lemon Volume for } \$24 = \frac{24}{4/3} = 24 \times \frac{3}{4} = 18\text{ lemons.}$$

Question 6

6. A trader gives a discount of $10\%$ on the marked price. To gain $17\%$, by what percentage must he mark up his goods over the cost price?

A) $27\%$

B) $30\%$

C) $33\%$

D) $35\%$

Answer

Correct Answer: B

Solution: Let $\text{CP} = 100$. Target Profit = $17\% \implies \text{SP} = 117$. Let Marked Price be $\text{MP}$. Given a discount factor of $10\%$: $$0.90 \times \text{MP} = 117 \implies \text{MP} = \frac{117}{0.9} = 130.$$ $$\text{Markup Value} = 130 - 100 = 30\%.$$

Question 7

7. A man sells two articles for $\$990$ each. On one he gains $10\%$ and on the other he loses $10\%$. What is his total gain or loss?

A) Loss of $\$20$

B) Gain of $\$20$

C) Loss of $1\%$ but no dollar value change

D) No profit, no loss

Answer

Correct Answer: A

Solution: * Article 1 (Gain): $\text{SP} = 990, \text{ Gain} = 10\% \implies \text{CP}_1 = \frac{990}{1.1} = 900$. * Article 2 (Loss): $\text{SP} = 990, \text{ Loss} = 10\% \implies \text{CP}_2 = \frac{990}{0.9} = 1100$. Total cost asset pool $\text{CP} = 900 + 1100 = 2000$. Total revenue output $\text{SP} = 990 + 990 = 1980$. $$\text{Net Loss} = \text{Total CP} - \text{Total SP} = 2000 - 1980 = \$20.$$

Question 8

8. If the selling price of an article is doubled, the profit triples. What was the original profit percentage?

A) $50\%$

B) $75\%$

C) $120\%$

D) $100\%$

Answer

Correct Answer: D

Solution: Let $\text{CP} = x$ and initial $\text{SP} = y$. Initial profit setup $P = y - x$. New selling threshold $= 2y \implies \text{New Profit} = 2y - x$. According to the constraints: $$2y - x = 3(y - x)$$ $$2y - x = 3y - 3x \implies y = 2x.$$ Substituting back shows original profit $= y - x = 2x - x = x$. $$\text{Original Profit Percentage} = \left(\frac{x}{x}\right) \times 100 = 100\%.$$

Question 9

9. The cost price of $15$ articles is equal to the selling price of $12$ articles. Find the profit or loss percentage.

A) $25\%$ Gain

B) $20\%$ Gain

C) $25\%$ Loss

D) $20\%$ Loss

Answer

Correct Answer: A

Solution: $$15 \times \text{CP} = 12 \times \text{SP} \implies \frac{\text{SP}}{\text{CP}} = \frac{15}{12} = \frac{5}{4}.$$ Assigning ratios, let $\text{CP} = 4$ and $\text{SP} = 5$. Profit Margin Amount $= 5 - 4 = 1$. $$\text{Net Profit Percentage} = \left(\frac{1}{4}\right) \times 100 = 25\%\text{ Gain.}$$

Question 10

10. An offer says "Buy 5 Get 4 Free". Additionally, the shopkeeper gives a $20\%$ cash discount. What is the total effective discount percentage?

A) $44.44\%$

B) $55.55\%$

C) $60\%$

D) $52.5\%$

Answer

Correct Answer: B

Solution: Total item allocation inventory given $= 5 + 4 = 9\text{ articles}$. Free product units component $= 4$. $$\text{Primary Product Discount Percentage} = \left(\frac{4}{9}\right) \times 100 = 44.44\%.$$ Remaining asset baseline value factor $= 100\% - 44.44\% = 55.56\%$. Additional $20\%$ sequential cash discount on remaining value $= 55.56 \times 0.20 = 11.11\%$. $$\text{Total Effective Discount} = 44.44\% + 11.11\% = 55.55\%.$$

Accepted Answer

Correct Answer: D

Solution: Let $\text{SP} = 100$. Profit Margin = $20\% \text{ of } 100 = 20$. $\text{CP} = \text{SP} - \text{Profit} = 100 - 20 = 80$. $$\text{Actual Profit Percentage (on CP)} = \left(\frac{20}{80}\right) \times 100 = 25\%.$$

Competitive Exams : Quantitative Aptitude - Profit/Loss (Set 2) | Concept of Maths

Competitive Exams : Quantitative Aptitude - Profit/Loss (Set 2) | Concept of Maths

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4. A sold an item to B at a gain of $20\%$. B sold it to C at a loss of $10\%$. If C paid $\$1080$ for it, at what price did A purchase the item?

5. By selling $45$ lemons for $\$40$, a man loses $20\%$. How many lemons should he sell for $\$24$ to gain $20\%$ in the transaction?

6. A trader gives a discount of $10\%$ on the marked price. To gain $17\%$, by what percentage must he mark up his goods over the cost price?

7. A man sells two articles for $\$990$ each. On one he gains $10\%$ and on the other he loses $10\%$. What is his total gain or loss?

8. If the selling price of an article is doubled, the profit triples. What was the original profit percentage?

9. The cost price of $15$ articles is equal to the selling price of $12$ articles. Find the profit or loss percentage.

10. An offer says "Buy 5 Get 4 Free". Additionally, the shopkeeper gives a $20\%$ cash discount. What is the total effective discount percentage?

Profit and Loss Quiz (Set 2) | Concept of Maths Ranchi

1. A manufacturer marks an article $40\%$ above the cost price and allows two successive discounts of $10\%$ and $5\%$ to a retailer. What is the net profit percentage for the manufacturer?

2. A dishonest shopkeeper claims to sell his goods at a loss of $4\%$, but he uses a weight of $900$ grams instead of $1\text{ kg}$. What is his actual profit percentage?

3. If a merchant estimates his profit as $20\%$ of the selling price, what is his actual profit percentage calculated on the cost price?

Competitive Exams : Quantitative Aptitude - Profit/Loss (Set 2) | Concept of Maths

Competitive Exams : Quantitative Aptitude - Profit/Loss (Set 2) | Concept of Maths

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4. A sold an item to B at a gain of $20\%$. B sold it to C at a loss of $10\%$. If C paid $\$1080$ for it, at what price did A purchase the item?

5. By selling $45$ lemons for $\$40$, a man loses $20\%$. How many lemons should he sell for $\$24$ to gain $20\%$ in the transaction?

6. A trader gives a discount of $10\%$ on the marked price. To gain $17\%$, by what percentage must he mark up his goods over the cost price?

7. A man sells two articles for $\$990$ each. On one he gains $10\%$ and on the other he loses $10\%$. What is his total gain or loss?

8. If the selling price of an article is doubled, the profit triples. What was the original profit percentage?

9. The cost price of $15$ articles is equal to the selling price of $12$ articles. Find the profit or loss percentage.

10. An offer says "Buy 5 Get 4 Free". Additionally, the shopkeeper gives a $20\%$ cash discount. What is the total effective discount percentage?