Advanced Profit and Loss Quiz | Competitive Exams Ranchi | Concept of Maths

Question 1

1. A hardware startup imports 800 high-precision LiDAR sensors. 15% of the sensors are damaged during transit and cannot be sold. The startup spends Rs 10,000 on customs and logistics for the entire batch. If the cost price of one sensor is Rs 120 and the startup wants a net profit of 20% on the total investment, at what price should each of the remaining sensors be sold?

A) Rs 174.50

B) Rs 182.15

C) Rs 187.06

D) Rs 192.40

Answer

Correct Answer: C

Total Cost Price (CP) = $(800 \times 120) + 10,000 = 96,000 + 10,000 = 106,000$. Desired Profit = 20% of 106,000 = $0.20 \times 106,000 = 21,200$. Total Desired Revenue (SP) = $106,000 + 21,200 = 127,200$. Number of sellable sensors = $800 - (15\% \text{ of } 800) = 800 - 120 = 680$. Selling Price per sensor = $$\frac{127,200}{680} \approx 187.058...$$ Rounded to Rs 187.06

Question 2

2. A dishonest grain merchant marks up his organic quinoa by 40% above the cost price. He then offers a discount of 10% to customers. However, while selling, he uses a rigged electronic scale that weighs only 850 grams for every 1000 grams. What is his actual overall profit percentage?

A) 44.12%

B) 48.24%

C) 52.35%

D) 41.18%

Answer

Correct Answer: B

Let CP of 1000g be $100. Marked Price (MP) = $100 + 40\% = 140$. Selling Price (SP) after 10% discount = $140 \times 0.90 = 126$. This SP is for 1000g (as per the customer's belief), but the merchant only gives 850g. Actual CP of 850g given = $$\frac{100}{1000} \times 850 = 85$$. Profit = $SP - \text{Actual CP} = 126 - 85 = 41$. Profit % = $$\frac{41}{85} \times 100 \approx 48.235...\%$$

Question 3

3. A refurbished laptop dealer buys a machine for Rs 450. He spends 20% of the purchase price on upgrades (RAM and SSD). He then sells it to a customer at a profit of 25%. The customer, after using it for a month, sells it back to the dealer at a loss of 30%. If the dealer then sells the same laptop to another buyer for Rs 600, what is the dealer's net profit from all transactions combined?

Question 4

4. A real estate developer sells a penthouse at a profit of 15%. If he had purchased it for 5% less and sold it for $18,750 more, he would have gained 25%. What was the original cost price of the penthouse?

A) $500,000

B) $450,000

C) $550,000

D) $600,000

Answer

Correct Answer: A

Let original CP be $x$. Original SP (15% profit) = $1.15x$. New CP (5% less) = $0.95x$. New SP = $1.15x + 18,750$. New Profit is 25% on the New CP: $$New SP = New CP \times 1.25$$ $$1.15x + 18,750 = 0.95x \times 1.25$$ $$1.15x + 18,750 = 1.1875x$$ $$18,750 = 0.0375x$$ $$x = \frac{18,750}{0.0375} = 500,000$$.

Question 5

5. A wholesale dealer of chemical reagents offers a successive discount of 15% and 10% on the marked price of a bulk order. Additionally, a 5% tax is applied on the discounted price. If a research lab pays $8,042.25 for the order, what was the original marked price?

A) $9,500

B) $10,000

C) $10,500

D) $11,000

Answer

Correct Answer: B

Let Marked Price (MP) be $M. Price after 15% discount: $0.85M$. Price after subsequent 10% discount: $0.85M \times 0.90 = 0.765M$. Price after adding 5% tax: $0.765M \times 1.05 = 0.80325M$. Given Final Price = $8,042.25$. $$0.80325M = 8,042.25$$ $$M = \frac{8,042.25}{0.80325} = 10,000$$.

Question 6

6. A cryptocurrency trader buys Bitcoin (BTC) and Ethereum (ETH) in the ratio of 3:5 by value. Within a week, BTC gains 20% in value, while ETH loses 8%. The trader sells both and realizes a total profit of $4,000. What was the initial amount invested in Bitcoin?

A) $60,000

B) $100,000

C) $120,000

D) $150,000

Answer

Correct Answer: A

Let initial investment in BTC be $3x$ and ETH be $5x$. Profit from BTC = $20\% \text{ of } 3x = 0.6x$. Loss from ETH = $8\% \text{ of } 5x = 0.4x$. Total Net Profit = $0.6x - 0.4x = 0.2x$. Given Net Profit = $4,000$. $$0.2x = 4,000 \implies x = 20,000$$ Initial BTC Investment = $3x = 3 \times 20,000 = 60,000$.

Question 7

7. An electronics retailer buys 50 smartphones at $400 each. He sells 20 of them at a profit of 15%. At what profit percentage must he sell the remaining 30 smartphones to achieve an overall profit of 25% on the entire stock?

A) 28.5%

B) 30.0%

C) 31.67%

D) 33.33%

Answer

Correct Answer: C

Total Cost Price (CP) = $50 \times 400 = 20,000$. Desired Total Selling Price (SP) for 25% overall profit = $20,000 \times 1.25 = 25,000$. SP of first 20 phones (sold at 15% profit) = $20 \times 400 \times 1.15 = 9,200$. Revenue still needed from remaining phones = $25,000 - 9,200 = 15,800$. CP of remaining 30 phones = $30 \times 400 = 12,000$. Required Profit on remaining phones = $15,800 - 12,000 = 3,800$. Required Profit % = $$\frac{3,800}{12,000} \times 100 \approx 31.67\%$$.

Question 8

8. A manufacturer of solar panels finds that the cost of production is divided into Raw Materials (50%), Labor (30%), and Overheads (20%). If the price of raw materials increases by 20%, labor costs increase by 10%, and overheads decrease by 15%, by what percentage must the selling price be increased to maintain the same profit margin of 20% on the cost?

A) 10%

B) 12%

C) 15%

D) 8%

Answer

Correct Answer: A

Let the original Total Cost be $100$. Raw Materials = $50$, Labor = $30$, Overheads = $20$. New Raw Materials = $50 \times 1.20 = 60$. New Labor = $30 \times 1.10 = 33$. New Overheads = $20 \times 0.85 = 17$. New Total Cost = $60 + 33 + 17 = 110$. Since the profit margin percentage (20% on cost) is constant: Original SP = $100 \times 1.20 = 120$. New SP = $110 \times 1.20 = 132$. Increase in SP = $132 - 120 = 12$. Percentage increase = $$\frac{12}{120} \times 100 = 10\%$$.

Question 9

9. A textile mill marks its fabric 60% above the cost price. It sells one-third of the fabric at the marked price, one-third at a discount of 10%, and the rest at a discount of 50%. What is the mill's overall profit percentage on the entire stock?

A) 24%

B) 28%

C) 32%

D) 36%

Answer

Correct Answer: B

Let total quantity be 3 units and Cost Price (CP) per unit be $100. Total CP = $300. Marked Price (MP) per unit = $100 + 60\% = 160$. 1. First unit (1/3) sold at MP: SP = $160$. 2. Second unit (1/3) sold at 10% discount: SP = $160 \times 0.90 = 144$. 3. Third unit (rest) sold at 50% discount: SP = $160 \times 0.50 = 80$. Total Selling Price (SP) = $160 + 144 + 80 = 384$. Total Profit = $384 - 300 = 84$. Profit % = $$\frac{84}{300} \times 100 = 28\%$$.

Question 10

10. An antique clock is sold for $288. The numerical value of the profit percentage is exactly half the numerical value of the cost price in dollars. What is the cost price of the clock?

A) $120

B) $150

C) $160

D) $180

Answer

Correct Answer: C

Let Cost Price (CP) = $x$. Profit % = $x/2$. Selling Price (SP) = $CP + \text{Profit} = x + \left(\frac{x/2}{100}\right)x = x + \frac{x^2}{200}$. Given SP = $288$. $$x + \frac{x^2}{200} = 288$$ Multiply the equation by 200: $$x^2 + 200x - 57,600 = 0$$ Factoring the quadratic equation: $$(x - 160)(x + 360) = 0$$ Since price cannot be negative, $x = 160$. The CP is $160$.

Question 11

11. A fruit vendor buys a crate of 200 mangoes at $2 per mango. 10% of the mangoes are found to be rotten. He sells the good mangoes at a price such that even if he gives 1 mango free with every purchase of 4 mangoes, he still makes an overall profit of 35%. What is the selling price he quotes per mango?

A) $3.50

B) $3.75

C) $4.00

D) $4.25

Answer

Correct Answer: B

Total Cost Price (CP) = $200 \times 2 = 400$. Total Desired SP (for 35% profit) = $400 \times 1.35 = 540$. Sellable (Good) mangoes = $200 - 10\% = 180$. The offer is "Buy 4, get 1 free". This means out of every 5 mangoes that leave his cart, only 4 are paid for. Number of "chargeable" mangoes out of 180 = $180 \times \left(\frac{4}{5}\right) = 144$. Required Selling Price per mango = $$\frac{540}{144} = 3.75$$.

Question 12

12. A company produces a gadget where the ratio of Cost Price to Marked Price is 3:5. The gadget is sold at a discount of 20%. If the company's profit is $150 per gadget, what is the Cost Price?

A) $450

B) $300

C) $600

D) $750

Answer

Correct Answer: A

Let Cost Price (CP) = $3x$ and Marked Price (MP) = $5x$. Discount = 20% of MP = $0.20 \times 5x = x$. Selling Price (SP) = MP - Discount = $5x - x = 4x$. Profit = $SP - CP = 4x - 3x = x$. Given Profit = $150$. So $x = 150$. Therefore, Cost Price (CP) = $3x = 3 \times 150 = 450$.

Question 13

13. By selling 120 meters of cloth, a merchant gains the cost price of 30 meters. If the merchant instead gained the selling price of 30 meters, what would be the difference between the two profit percentages?

A) 5%

B) 8.33%

C) 10%

D) 6.67%

Answer

Correct Answer: B

Case 1: Profit = CP of 30m. Profit % = $$\frac{30 \times CP}{120 \times CP} \times 100 = 25\%$$. Case 2: Profit = SP of 30m. Profit = $(120 \times SP) - (120 \times CP) = 30 \times SP$. $$90 \times SP = 120 \times CP \implies SP = \frac{120}{90}CP = \frac{4}{3}CP$$. Profit % = $$\frac{SP - CP}{CP} \times 100 = \frac{4/3 - 1}{1} \times 100 = 33.33\%$$. Difference = $33.33\% - 25\% = 8.33\%$.

Question 14

14. A dealer offers a cash discount of 12%. If the buyer chooses to pay in installments, the dealer adds a 10% surcharge on the marked price and then allows a 5% discount on the new total. What is the percentage difference between the cash price and the installment price relative to the marked price?

A) 12.5%

B) 14.2%

C) 15.8%

D) 16.5%

Answer

Correct Answer: D

Let Marked Price (MP) = 100. Cash Price = $100 - 12\% = 88$. Installment base price = $100 + 10\% \text{ surcharge} = 110$. Installment final price = $110 - 5\% \text{ discount} = 110 - 5.5 = 104.5$. Difference between final prices = $104.5 - 88 = 16.5$. Percentage relative to MP (100) = $$\frac{16.5}{100} \times 100 = 16.5\%$$.

Question 15

15. A tea blender mixes two varieties of tea: Variety A costing Rs 160/kg and Variety B costing Rs 260/kg. He mixes them in a ratio of 3:2. He sells the mixture at Rs 252/kg. However, his weighing machine shows 900g for every 1kg. What is his actual profit percentage?

A) 20%

B) 35%

C) 40%

D) 45%

Answer

Correct Answer: C

Cost Price (CP) of 5kg mixture = $(3 \times 160) + (2 \times 260) = 480 + 520 = 1000$. True CP per kg = $1000 / 5 = 200$. Because of the faulty scale, he charges $252 (the price of 1kg) for only 900g. True Selling Price (SP) of 1000g (1kg) = $$\frac{252}{0.90} = 280$$. Profit per kg = $280 - 200 = 80$. Profit % = $$\frac{80}{200} \times 100 = 40\%$$.

Question 16

16. A trader buys a stock of goods. He sells 40% of the stock at a profit of 20%, and 50% of the remaining stock at a loss of 10%. At what profit percentage should he sell the final remaining goods to ensure he makes no profit and no loss on the entire transaction?

A) Profit of 16.67%

B) Loss of 16.67%

C) Profit of 15%

D) Loss of 15%

Answer

Correct Answer: B

Let the total stock be 100 units costing $1 each. Total CP = $100. 1. First batch: 40 units sold at 20% profit. SP = $40 \times 1.20 = 48$. 2. Second batch: 50% of remaining 60 units = 30 units. Sold at 10% loss. SP = $30 \times 0.90 = 27$. Total revenue so far = $48 + 27 = 75$. To break even (no profit, no loss), total revenue must equal total CP ($100). Revenue needed from the final 30 units = $100 - 75 = 25$. The CP of these final 30 units is $30$. He must sell them for $25$. Loss incurred = $30 - 25 = 5$. Loss % = $$\frac{5}{30} \times 100 = 16.67\%$$.

Question 17

17. An article is marked such that the profit is 20% even after allowing a discount of 20%. If the cost price of the article increases by 25% and the manufacturer wants to maintain the same marked price, what discount should he now offer to still make a profit of 10%?

A) 5%

B) 8.33%

C) 10%

D) 12.5%

Answer

Correct Answer: B

Let original Cost Price (CP) = 100. Profit is 20%, so original SP = 120. A 20% discount on Marked Price (MP) yields this SP: $$MP \times 0.80 = 120 \implies MP = 150$$. New CP (increased by 25%) = 125. Desired Profit is 10% on the New CP: $$\text{New SP} = 125 \times 1.10 = 137.50$$. Discount required from the static MP: $$\text{Discount} = 150 - 137.50 = 12.50$$. Discount % = $$\frac{12.50}{150} \times 100 = 8.33\%$$.

Question 18

18. A trader calculates his profit percentage on the selling price and finds it to be 20%. If he had calculated it on the cost price, and the cost price then decreased by 10% while the selling price remained the same, what would be his new profit percentage on the cost price?

A) 25%

B) 33.33%

C) 38.89%

D) 42.15%

Answer

Correct Answer: C

Initial Profit is 20% of the Selling Price (SP). Let SP = 100. Initial Profit = 20. Initial Cost Price (CP) = $100 - 20 = 80$. New CP (decreased by 10%) = $80 \times 0.90 = 72$. SP remains 100. New actual Profit = $100 - 72 = 28$. New Profit % on CP = $$\frac{28}{72} \times 100 = 38.888...\%$$

Question 19

19. A person sells a machine at a gain of 10%. If he had sold it for Rs 80 less, he would have lost 10%. If he sells it for Rs 480, what is his profit or loss percentage?

A) 15% profit

B) 20% profit

C) 20% loss

D) 25% profit

Answer

Correct Answer: B

Let Cost Price (CP) be $x$. Selling Price 1 (10% profit) = $1.10x$. Selling Price 2 (10% loss) = $0.90x$. Difference in SPs = $80$. $$1.10x - 0.90x = 80 \implies 0.20x = 80 \implies x = 400$$. CP is $400$. If new SP = $480. Profit = $480 - 400 = 80$. Profit % = $$\frac{80}{400} \times 100 = 20\%$$.

Question 20

20. A shopkeeper gives 3 items free on the purchase of every 12 items. He also allows a further discount of 25% to the customer and still makes a profit of 20%. Find the ratio of the Cost Price to the Marked Price of one item.

A) 1:2

B) 2:3

C) 3:4

D) 3:5

Answer

Correct Answer: A

"Buy 12, get 3 free" means the customer walks away with 15 items but the base price is only evaluated on 12. Let Marked Price (MP) of 1 item be $1. Total MP for the 12 items charged = $12. Price after 25% discount on those 12 items = $12 \times 0.75 = 9$. So, the Final Selling Price (SP) for all 15 items combined = $9$. The shopkeeper still makes a 20% profit on his overall Cost Price (CP): $$1.20 \times \text{Total CP of 15 items} = 9 \implies \text{Total CP} = 7.50$$. CP per item = $7.50 / 15 = 0.50$. Ratio of CP to MP = $0.50 : 1 = 1:2$.

Accepted Answer

Correct Answer: D

1. Initial CP = Rs 450. Upgrades = $450 \times 0.20 = 90$. Total Dealer CP1 = $540$. 2. Sold to Customer at 25% profit: $SP_1 = 540 \times 1.25 = 675$. Dealer's first profit = $675 - 540 = 135$. 3. Customer sells back at 30% loss: Dealer CP2 = $675 \times 0.70 = 472.50$. 4. Dealer sells to new buyer for Rs 600: Dealer's second profit = $600 - 472.50 = 127.50$. Net Profit = First Profit + Second Profit = $135 + 127.50 = 262.50$.

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 real estate developer sells a penthouse at a profit of 15%. If he had purchased it for 5% less and sold it for $18,750 more, he would have gained 25%. What was the original cost price of the penthouse?

5. A wholesale dealer of chemical reagents offers a successive discount of 15% and 10% on the marked price of a bulk order. Additionally, a 5% tax is applied on the discounted price. If a research lab pays $8,042.25 for the order, what was the original marked price?

6. A cryptocurrency trader buys Bitcoin (BTC) and Ethereum (ETH) in the ratio of 3:5 by value. Within a week, BTC gains 20% in value, while ETH loses 8%. The trader sells both and realizes a total profit of $4,000. What was the initial amount invested in Bitcoin?

7. An electronics retailer buys 50 smartphones at $400 each. He sells 20 of them at a profit of 15%. At what profit percentage must he sell the remaining 30 smartphones to achieve an overall profit of 25% on the entire stock?

9. A textile mill marks its fabric 60% above the cost price. It sells one-third of the fabric at the marked price, one-third at a discount of 10%, and the rest at a discount of 50%. What is the mill's overall profit percentage on the entire stock?

10. An antique clock is sold for $288. The numerical value of the profit percentage is exactly half the numerical value of the cost price in dollars. What is the cost price of the clock?

12. A company produces a gadget where the ratio of Cost Price to Marked Price is 3:5. The gadget is sold at a discount of 20%. If the company's profit is $150 per gadget, what is the Cost Price?

13. By selling 120 meters of cloth, a merchant gains the cost price of 30 meters. If the merchant instead gained the selling price of 30 meters, what would be the difference between the two profit percentages?

15. A tea blender mixes two varieties of tea: Variety A costing Rs 160/kg and Variety B costing Rs 260/kg. He mixes them in a ratio of 3:2. He sells the mixture at Rs 252/kg. However, his weighing machine shows 900g for every 1kg. What is his actual profit percentage?

16. A trader buys a stock of goods. He sells 40% of the stock at a profit of 20%, and 50% of the remaining stock at a loss of 10%. At what profit percentage should he sell the final remaining goods to ensure he makes no profit and no loss on the entire transaction?

17. An article is marked such that the profit is 20% even after allowing a discount of 20%. If the cost price of the article increases by 25% and the manufacturer wants to maintain the same marked price, what discount should he now offer to still make a profit of 10%?

18. A trader calculates his profit percentage on the selling price and finds it to be 20%. If he had calculated it on the cost price, and the cost price then decreased by 10% while the selling price remained the same, what would be his new profit percentage on the cost price?

19. A person sells a machine at a gain of 10%. If he had sold it for Rs 80 less, he would have lost 10%. If he sells it for Rs 480, what is his profit or loss percentage?

20. A shopkeeper gives 3 items free on the purchase of every 12 items. He also allows a further discount of 25% to the customer and still makes a profit of 20%. Find the ratio of the Cost Price to the Marked Price of one item.

Advanced Profit and Loss Quiz | Competitive Exams Ranchi | Concept of Maths

2. A dishonest grain merchant marks up his organic quinoa by 40% above the cost price. He then offers a discount of 10% to customers. However, while selling, he uses a rigged electronic scale that weighs only 850 grams for every 1000 grams. What is his actual overall profit percentage?

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 real estate developer sells a penthouse at a profit of 15%. If he had purchased it for 5% less and sold it for $18,750 more, he would have gained 25%. What was the original cost price of the penthouse?

5. A wholesale dealer of chemical reagents offers a successive discount of 15% and 10% on the marked price of a bulk order. Additionally, a 5% tax is applied on the discounted price. If a research lab pays $8,042.25 for the order, what was the original marked price?

6. A cryptocurrency trader buys Bitcoin (BTC) and Ethereum (ETH) in the ratio of 3:5 by value. Within a week, BTC gains 20% in value, while ETH loses 8%. The trader sells both and realizes a total profit of $4,000. What was the initial amount invested in Bitcoin?

7. An electronics retailer buys 50 smartphones at $400 each. He sells 20 of them at a profit of 15%. At what profit percentage must he sell the remaining 30 smartphones to achieve an overall profit of 25% on the entire stock?

9. A textile mill marks its fabric 60% above the cost price. It sells one-third of the fabric at the marked price, one-third at a discount of 10%, and the rest at a discount of 50%. What is the mill's overall profit percentage on the entire stock?

10. An antique clock is sold for $288. The numerical value of the profit percentage is exactly half the numerical value of the cost price in dollars. What is the cost price of the clock?

12. A company produces a gadget where the ratio of Cost Price to Marked Price is 3:5. The gadget is sold at a discount of 20%. If the company's profit is $150 per gadget, what is the Cost Price?

13. By selling 120 meters of cloth, a merchant gains the cost price of 30 meters. If the merchant instead gained the selling price of 30 meters, what would be the difference between the two profit percentages?

15. A tea blender mixes two varieties of tea: Variety A costing Rs 160/kg and Variety B costing Rs 260/kg. He mixes them in a ratio of 3:2. He sells the mixture at Rs 252/kg. However, his weighing machine shows 900g for every 1kg. What is his actual profit percentage?

16. A trader buys a stock of goods. He sells 40% of the stock at a profit of 20%, and 50% of the remaining stock at a loss of 10%. At what profit percentage should he sell the final remaining goods to ensure he makes no profit and no loss on the entire transaction?

17. An article is marked such that the profit is 20% even after allowing a discount of 20%. If the cost price of the article increases by 25% and the manufacturer wants to maintain the same marked price, what discount should he now offer to still make a profit of 10%?

18. A trader calculates his profit percentage on the selling price and finds it to be 20%. If he had calculated it on the cost price, and the cost price then decreased by 10% while the selling price remained the same, what would be his new profit percentage on the cost price?

19. A person sells a machine at a gain of 10%. If he had sold it for Rs 80 less, he would have lost 10%. If he sells it for Rs 480, what is his profit or loss percentage?

20. A shopkeeper gives 3 items free on the purchase of every 12 items. He also allows a further discount of 25% to the customer and still makes a profit of 20%. Find the ratio of the Cost Price to the Marked Price of one item.