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Profit, Loss & Discount

Cost price, selling price, marked price, discounts and false weights.

42 solved questions · 14 easy · 19 medium · 9 hard

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Shortcuts & formulas

  • Profit = SP - CP; Loss = CP - SP. Profit% = Profit/CP x 100 and Loss% = Loss/CP x 100 (always on cost price).
  • SP = CP x (100 + P)/100 for a profit of P%; SP = CP x (100 - L)/100 for a loss of L%.
  • Discount = MP - SP; Discount% = Discount/MP x 100. SP = MP x (100 - d)/100.
  • Two successive discounts a% and b% equal a single discount of a + b - ab/100 %.
  • Two articles sold at the same price, one at x% profit and the other at x% loss: overall loss = x^2/100 %.
  • False weight: Profit% = (True weight - False weight)/False weight x 100 (for a dealer who sells at cost price).
  • If the CP of x articles equals the SP of y articles, Profit% = (x - y)/y x 100.

Solved examples

Try each one first, then open the answer and the step-by-step solution.

Easy questions

Q1.

An article bought for ₹800 is sold at a profit of 25%. Find the selling price.

  1. A₹1,000
  2. B₹825
  3. C₹600
  4. D₹200
Show answer & solution

Answer: A. ₹1,000

Solution

Profit = 25% of 800 = ₹200 SP = CP + Profit = 800 + 200 = ₹1,000 Answer: ₹1,000

Q2.

An article bought for ₹1,250 is sold at a profit of 12%. Find the selling price.

  1. A₹1,262
  2. B₹1,100
  3. C₹150
  4. D₹1,400
Show answer & solution

Answer: D. ₹1,400

Solution

Profit = 12% of 1,250 = ₹150 SP = CP + Profit = 1,250 + 150 = ₹1,400 Answer: ₹1,400

Q3.

A chair costing ₹1,200 is sold at a loss of 20%. What is the selling price?

  1. A₹1,440
  2. B₹240
  3. C₹960
  4. D₹1,180
Show answer & solution

Answer: C. ₹960

Solution

Loss = 20% of 1,200 = ₹240 SP = 1,200 - 240 = ₹960 Answer: ₹960

Q4.

A trader buys a bag for ₹500 and sells it for ₹625. What is his profit percentage?

  1. A20%
  2. B25%
  3. C125%
  4. D30%
Show answer & solution

Answer: B. 25%

Solution

Profit = 625 - 500 = ₹125 Profit% = 125/500 x 100 = 25% Answer: 25%

Q5.

A watch bought for ₹400 is sold for ₹300. Find the loss percentage.

  1. A25%
  2. B33.33%
  3. C20%
  4. D75%
Show answer & solution

Answer: A. 25%

Solution

Loss = 400 - 300 = ₹100 Loss% = 100/400 x 100 = 25% Answer: 25%

Shortcut: Loss is on the cost price (400), not the selling price.

Q6.

The marked price of a table fan is ₹2,000 and a discount of 15% is given. What is the discount amount?

  1. A₹150
  2. B₹1,700
  3. C₹350
  4. D₹300
Show answer & solution

Answer: D. ₹300

Solution

Discount = 15% of 2,000 = ₹300 Answer: ₹300

Q7.

A pair of shoes is marked at ₹1,500 and sold at ₹1,275. What is the discount percentage?

  1. A225%
  2. B17%
  3. C15%
  4. D10%
Show answer & solution

Answer: C. 15%

Solution

Discount = 1,500 - 1,275 = ₹225 Discount% = 225/1,500 x 100 = 15% Answer: 15%

Q8.

By selling a bicycle for ₹1,320 a shopkeeper gains 10%. What is the cost price?

  1. A₹1,188
  2. B₹1,200
  3. C₹1,452
  4. D₹1,310
Show answer & solution

Answer: B. ₹1,200

Solution

SP = 110% of CP = 1,320 CP = 1,320 x 100/110 = ₹1,200 Answer: ₹1,200

Q9.

A man sells a radio for ₹1,080 at a loss of 10%. What did the radio cost him?

  1. A₹1,200
  2. B₹972
  3. C₹1,188
  4. D₹1,190
Show answer & solution

Answer: A. ₹1,200

Solution

SP = 90% of CP = 1,080 CP = 1,080 x 100/90 = ₹1,200 Answer: ₹1,200

Q10.

A refrigerator marked at ₹18,000 is sold at a discount of 25%. Find the selling price.

  1. A₹4,500
  2. B₹22,500
  3. C₹13,050
  4. D₹13,500
Show answer & solution

Answer: D. ₹13,500

Solution

Discount = 25% of 18,000 = ₹4,500 SP = 18,000 - 4,500 = ₹13,500 Answer: ₹13,500

Q11.

A dozen pens cost ₹240 and are all sold for ₹300. Find the profit per pen.

  1. A₹20
  2. B₹25
  3. C₹5
  4. D₹60
Show answer & solution

Answer: C. ₹5

Solution

Total profit = 300 - 240 = ₹60 Profit per pen = 60/12 = ₹5 Answer: ₹5

Q12.

A fruit seller buys apples at ₹80 per kg and sells at ₹92 per kg. What is his profit percentage?

  1. A12%
  2. B15%
  3. C13%
  4. D11.5%
Show answer & solution

Answer: B. 15%

Solution

Profit per kg = 92 - 80 = ₹12 Profit% = 12/80 x 100 = 15% Answer: 15%

Q13.

If the selling price of an article is ₹720 and the profit is ₹120, what is the cost price?

  1. A₹600
  2. B₹840
  3. C₹720
  4. D₹660
Show answer & solution

Answer: A. ₹600

Solution

CP = SP - Profit = 720 - 120 = ₹600 Answer: ₹600

Q14.

A bookseller allows a 10% discount on a book marked ₹350. How much does a customer pay?

  1. A₹35
  2. B₹340
  3. C₹385
  4. D₹315
Show answer & solution

Answer: D. ₹315

Solution

Discount = 10% of 350 = ₹35 Price paid = 350 - 35 = ₹315 Answer: ₹315

Medium questions

Q15.

A shopkeeper marks his goods 40% above cost price and then allows a discount of 20%. What is his profit percentage?

  1. A20%
  2. B8%
  3. C12%
  4. D14%
Show answer & solution

Answer: C. 12%

Solution

Let CP = 100 MP = 140 SP = 140 x 0.80 = 112 Profit = 12% Answer: 12%

Q16.

What single discount is equal to two successive discounts of 20% and 10%?

  1. A30%
  2. B28%
  3. C25%
  4. D27%
Show answer & solution

Answer: B. 28%

Solution

Net = 20 + 10 - (20 x 10)/100 = 30 - 2 = 28% Or: 100 x 0.8 x 0.9 = 72, so the discount is 28% Answer: 28%

Shortcut: Never add successive discounts; subtract the product term.

Q17.

Two articles are sold at ₹1,200 each. One is sold at a 20% profit and the other at a 20% loss. Find the overall result.

  1. ALoss of 4%
  2. BNo profit, no loss
  3. CGain of 4%
  4. DGain of 2%
Show answer & solution

Answer: A. Loss of 4%

Solution

CP of first = 1,200 x 100/120 = ₹1,000 CP of second = 1,200 x 100/80 = ₹1,500 Total CP = 2,500; total SP = 2,400 Loss = 100, Loss% = 100/2,500 x 100 = 4% Answer: Loss of 4%

Shortcut: Equal SP with x% gain and x% loss: always a loss of x^2/100 = 400/100 = 4%.

Q18.

If the cost price of 15 articles equals the selling price of 12 articles, what is the profit percentage?

  1. A20%
  2. B15%
  3. C30%
  4. D25%
Show answer & solution

Answer: D. 25%

Solution

Let the price of 1 article at CP be 1 CP of 12 articles = 12; SP of 12 articles = CP of 15 = 15 Profit = 3 Profit% = 3/12 x 100 = 25% Answer: 25%

Shortcut: (x - y)/y = (15 - 12)/12 = 25%.

Q19.

A dealer sells 1 kg of sugar using a false weight of 800 g and takes the price of 1 kg. Find his gain percentage.

  1. A20%
  2. B30%
  3. C25%
  4. D80%
Show answer & solution

Answer: C. 25%

Solution

He gives 800 g but charges for 1,000 g Gain = 200 g on a cost of 800 g Gain% = 200/800 x 100 = 25% Answer: 25%

Shortcut: Gain% = (error/true value given) x 100 = (200/800) x 100.

Q20.

A shopkeeper buys 6 pencils for ₹5 and sells 5 pencils for ₹6. What is his profit percentage?

  1. A20%
  2. B44%
  3. C36%
  4. D40%
Show answer & solution

Answer: B. 44%

Solution

CP of 30 pencils = 5 x 5 = ₹25 SP of 30 pencils = 6 x 6 = ₹36 Profit = 11 Profit% = 11/25 x 100 = 44% Answer: 44%

Q21.

A trader wants a profit of 20% on goods costing ₹2,000 after giving a 20% discount on the marked price. What should the marked price be?

  1. A₹3,000
  2. B₹2,400
  3. C₹2,880
  4. D₹2,500
Show answer & solution

Answer: A. ₹3,000

Solution

SP = 2,000 x 1.20 = ₹2,400 SP = 80% of MP MP = 2,400 x 100/80 = ₹3,000 Answer: ₹3,000

Q22.

A shop offers 'Buy 3, get 1 free' on a shirt. What is the effective discount percentage?

  1. A33%
  2. B20%
  3. C30%
  4. D25%
Show answer & solution

Answer: D. 25%

Solution

Customer pays for 3 shirts but gets 4 Discount = 1/4 of the value = 25% Answer: 25%

Q23.

A man sells an article at a 10% loss for ₹900. At what price must he sell it to gain 20%?

  1. A₹1,080
  2. B₹1,100
  3. C₹1,200
  4. D₹1,000
Show answer & solution

Answer: C. ₹1,200

Solution

CP = 900 x 100/90 = ₹1,000 SP for 20% gain = 1,000 x 1.20 = ₹1,200 Answer: ₹1,200

Q24.

Two articles are sold at the same price, one at a 25% gain and the other at a 25% loss. What is the overall loss percentage?

  1. A25%
  2. B6.25%
  3. C0%
  4. D5%
Show answer & solution

Answer: B. 6.25%

Solution

Overall loss = x^2/100 = 625/100 = 6.25% Answer: 6.25%

Q25.

If the cost price of 20 articles equals the selling price of 16 articles, find the profit percentage.

  1. A25%
  2. B20%
  3. C24%
  4. D30%
Show answer & solution

Answer: A. 25%

Solution

Let CP of 1 article = 1, so CP of 20 articles = 20 = SP of 16 articles CP of 16 = 16 units, SP of 16 = 20 units Profit = 4/16 x 100 = 25% Answer: 25%

Q26.

A trader sells 40% of his goods at a 20% profit and the remaining 60% at a 10% loss. What is his overall profit or loss?

  1. ALoss of 2%
  2. BProfit of 5%
  3. CProfit of 1%
  4. DProfit of 2%
Show answer & solution

Answer: D. Profit of 2%

Solution

Let total CP = 100 SP of 40 part = 40 x 1.2 = 48 SP of 60 part = 60 x 0.9 = 54 Total SP = 102 Profit = 2% Answer: Profit of 2%

Q27.

A shopkeeper marks a jacket 30% above cost and gives a 10% discount. If the jacket cost him ₹2,000, find his profit.

  1. A₹260
  2. B₹600
  3. C₹340
  4. D₹400
Show answer & solution

Answer: C. ₹340

Solution

MP = 2,000 x 1.30 = ₹2,600 SP = 2,600 x 0.90 = ₹2,340 Profit = 2,340 - 2,000 = ₹340 Answer: ₹340

Q28.

By selling an article for ₹1,260 a man gains 5%. What would be his gain or loss percentage if he sold it for ₹1,080?

  1. AGain of 10%
  2. BLoss of 10%
  3. CLoss of 5%
  4. DGain of 8%
Show answer & solution

Answer: B. Loss of 10%

Solution

CP = 1,260 x 100/105 = ₹1,200 SP = 1,080, loss = 120 Loss% = 120/1,200 x 100 = 10% Answer: Loss of 10%

Q29.

A television is marked at ₹24,000. A customer gets two successive discounts of 10% and 5%. What does he pay?

  1. A₹20,520
  2. B₹20,400
  3. C₹20,000
  4. D₹21,600
Show answer & solution

Answer: A. ₹20,520

Solution

After 10%: 24,000 x 0.90 = 21,600 After 5%: 21,600 x 0.95 = 20,520 Answer: ₹20,520

Q30.

A dealer sells a kettle at ₹1,380 after allowing a 8% discount. What is the marked price?

  1. A₹1,490
  2. B₹1,590
  3. C₹1,450
  4. D₹1,500
Show answer & solution

Answer: D. ₹1,500

Solution

SP = 92% of MP = 1,380 MP = 1,380 x 100/92 = ₹1,500 Answer: ₹1,500

Q31.

The profit on an article sold for ₹1,150 is 15%. If the same article is sold for ₹1,000, what is the profit or loss percentage?

  1. AProfit of 5%
  2. BLoss of 5%
  3. CNo profit, no loss
  4. DProfit of 15%
Show answer & solution

Answer: C. No profit, no loss

Solution

CP = 1,150 x 100/115 = ₹1,000 Sold for ₹1,000 = CP No profit, no loss Answer: No profit, no loss

Q32.

A grocer mixes 30 kg of rice costing ₹40 per kg with 20 kg of rice costing ₹45 per kg and sells the mixture at ₹52.50 per kg. What is his profit percentage?

  1. A20%
  2. B25%
  3. C15%
  4. D30%
Show answer & solution

Answer: B. 25%

Solution

Total cost = 30 x 40 + 20 x 45 = 1,200 + 900 = ₹2,100 Cost per kg = 2,100/50 = ₹42 Profit per kg = 52.50 - 42 = ₹10.50 Profit% = 10.50/42 x 100 = 25% Answer: 25%

Q33.

A man buys a mobile at 20% below its list price of ₹15,000 and sells it at the list price. What is his gain percentage?

  1. A25%
  2. B20%
  3. C30%
  4. D15%
Show answer & solution

Answer: A. 25%

Solution

CP = 15,000 x 0.80 = ₹12,000 SP = ₹15,000 Gain = 3,000 Gain% = 3,000/12,000 x 100 = 25% Answer: 25%

Shortcut: Gain% is on the lower price: 20/80 = 25%.

Hard questions

Q34.

A dishonest dealer buys goods using a weight of 1,200 g for 1 kg and sells using a weight of 800 g for 1 kg. Find his overall profit percentage.

  1. A25%
  2. B40%
  3. C20%
  4. D50%
Show answer & solution

Answer: D. 50%

Solution

Let price per kg be Rs p Selling '1 kg' (actually 800 g) brings p Cost of that 800 g, bought at 1,200 g per p, = p x 800/1,200 = 2p/3 Profit = p - 2p/3 = p/3 Profit% = (p/3)/(2p/3) x 100 = 50% Answer: 50%

Shortcut: Profit% = (1200/800 - 1) x 100 = 50%.

Q35.

A shopkeeper marks goods 30% above cost and gives a discount of x% to earn a 4% profit. Find x.

  1. A26%
  2. B30%
  3. C20%
  4. D15%
Show answer & solution

Answer: C. 20%

Solution

Let CP = 100, MP = 130, SP = 104 Discount = 130 - 104 = 26 x = 26/130 x 100 = 20% Answer: 20%

Q36.

A showroom marks a sofa at ₹5,000 and gives successive discounts of 20%, 10% and 5%. What is the selling price?

  1. A₹3,500
  2. B₹3,420
  3. C₹3,750
  4. D₹3,425
Show answer & solution

Answer: B. ₹3,420

Solution

After 20%: 5,000 x 0.80 = 4,000 After 10%: 4,000 x 0.90 = 3,600 After 5%: 3,600 x 0.95 = 3,420 Answer: ₹3,420

Q37.

A sells an article to B at a 20% profit, and B sells it to C at a 25% profit. If C pays ₹1,800, what did A pay for it?

  1. A₹1,200
  2. B₹1,000
  3. C₹1,080
  4. D₹1,250
Show answer & solution

Answer: A. ₹1,200

Solution

C's price = CP of A x 1.20 x 1.25 = 1.5 x CP CP = 1,800/1.5 = ₹1,200 Answer: ₹1,200

Q38.

By selling an article for ₹1,440 a man loses 10%. At what price should he sell it to gain 15%?

  1. A₹1,556
  2. B₹1,800
  3. C₹1,656
  4. D₹1,840
Show answer & solution

Answer: D. ₹1,840

Solution

CP = 1,440 x 100/90 = ₹1,600 SP for 15% gain = 1,600 x 1.15 = ₹1,840 Answer: ₹1,840

Q39.

A discount of 25% on the marked price still gives a shopkeeper a 20% profit. By what percentage is the marked price above the cost price?

  1. A45%
  2. B50%
  3. C60%
  4. D55%
Show answer & solution

Answer: C. 60%

Solution

Let CP = 100, SP = 120 SP = 75% of MP, so MP = 120/0.75 = 160 MP is 60% above CP Answer: 60%

Q40.

Two watches are each sold for ₹1,980, one at a 10% profit and the other at a 10% loss. What is the net result?

  1. ANo profit, no loss
  2. BLoss of ₹40
  3. CLoss of ₹20
  4. DLoss of ₹198
Show answer & solution

Answer: B. Loss of ₹40

Solution

CP of first = 1,980 x 100/110 = ₹1,800 CP of second = 1,980 x 100/90 = ₹2,200 Total CP = 4,000; total SP = 3,960 Loss = ₹40 Answer: Loss of ₹40

Shortcut: Overall loss% = 10^2/100 = 1% of 4,000 = ₹40.

Q41.

A man sells an article at a 20% profit. Had he bought it for 10% less and sold it for ₹30 less, he would have gained 30%. Find the original cost price.

  1. A₹1,000
  2. B₹800
  3. C₹1,200
  4. D₹900
Show answer & solution

Answer: A. ₹1,000

Solution

Let CP = x, SP = 1.2x New CP = 0.9x, new SP = 1.30 x 0.9x = 1.17x 1.2x - 30 = 1.17x 0.03x = 30 x = ₹1,000 Answer: ₹1,000

Q42.

A shopkeeper marks goods 25% above cost and offers '5 articles for the price of 4'. What is his profit or loss percentage?

  1. AProfit of 25%
  2. BLoss of 20%
  3. CProfit of 5%
  4. DNo profit, no loss
Show answer & solution

Answer: D. No profit, no loss

Solution

Let CP of one article = 100, MP = 125 Customer pays for 4 = 4 x 125 = 500 and gets 5 articles CP of 5 articles = 500 SP = CP, so no profit, no loss Answer: No profit, no loss

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