Quantitative Aptitude

Profit, Loss and Discount

2,604 Questions
All Basic CP/SP Percentage Relationship 874 Marked Price, Markup, and Discount 786 Partial Sales and Multiple Transactions 338 Successive Discounts 218 Cost Price of X = Selling Price of Y 180 Faulty Weight or Measure 126 Equal Profit and Loss Rates 57 Free-item Offers 23 Price and Consumption Variation 1

Profit, Loss and Discount Questions

Multiple choice

Ranjeet mix 4 liter water in 20 liter milk and sells whole mixture at 20% above cost price of milk. Find his overall profit percentage.

  1. 36%

  2. 28%

  3. 44%

  4. 48%

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ranjeet mixes 4 liters of water in 20 liters of milk, creating a 24-liter mixture. He sells the entire mixture at 20% above the cost price of milk. Cost price = 20 × milk cost per liter. Selling price = 24 × 1.2 × milk cost per liter = 28.8 × milk cost per liter. Profit = 28.8 - 20 = 8.8 × milk cost per liter. Profit percentage = (8.8/20) × 100 = 44%. Option C (44%) is correct. Options A (36%), B (28%), and D (48%) are incorrect calculations.

Multiple choice

A shopkeeper marks his goods 20% above the cost price, but allows 30% discount on cash payment. His net profit or loss% is- एक दुकानदार अपने सामान को क्रय मूल्य से 20% अधिक अंकित करता है, लेकिन नकद भुगतान पर 30% की छूट देता है। उसका कुल लाभ या हानि प्रतिशत है-

  1. 8%

  2. 10%

  3. 16%

  4. 20%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = 100. Marked price = 120. After 30% discount: SP = 120 × 0.70 = 84. Since CP = 100, this is a loss of 16%. Loss = 100 - 84 = 16. Always assume CP = 100 for percentage profit/loss problems.

Multiple choice

The ratio between cost price and selling price of an article is p : q. If q is 200% of p then the percentage of profit on cost price is- एक वस्तु के क्रय मूल्य और विक्रय मूल्य में अनुपात p : q है। यदि q, p का 200% है तो क्रय मूल्य पर लाभ प्रतिशतता है-

  1. 75%

  2. 125%

  3. 100%

  4. 200%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given CP:SP = p:q and q = 200% of p = 2p. So CP:SP = p:2p = 1:2, meaning SP = 2 × CP. Profit = SP - CP = 2CP - CP = CP. Profit percent on CP = (Profit/CP) × 100 = (CP/CP) × 100 = 100%. This is straightforward ratio and percentage problem. The key is understanding that 200% means 'twice' not '200% more'. The profit equals the cost price itself, giving 100% profit.

Multiple choice

If the profit percent got on selling an article is numerically equal to its cost price in rupees and the selling price is Rs. 39, then cost price (in Rs.) will be- यदि एक वस्तु को बेचने पर प्राप्त प्रतिशत लाभ का संख्यात्मक मान इसके क्रय मूल्य के बराबर है और विक्रय मूल्य 39 रू. है तो क्रय मूल्य (रू. में) होगा-

  1. 20

  2. 22

  3. 28

  4. 30
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP = x rupees. Given profit% = x (numerically equal to CP). Profit% = (Profit/CP) × 100 = (SP - x)/x × 100 = x. So (39 - x)/x × 100 = x. Solving: (39 - x) × 100 = x^2, so x^2 + 100x - 3900 = 0. Using quadratic formula: x = [-100 + √(10000 + 15600)]/2 = [-100 + √25600]/2 = [-100 + 160]/2 = 30. (Negative root rejected as CP > 0). Verification: CP=30, SP=39, Profit=9, Profit% = (9/30)×100 = 30%, which equals CP numerically.

Multiple choice

A trader allows two successive discount of 30% and 15% on selling an article. If he gets Rs.952 for that article, find its marked price. एक व्यापारी एक वस्तु को बेचने पर 30% और 15% की दो बार छूट की अनुमति देता है। यदि उस वस्तु के लिए उसे 952 रु. मिलते हैं, तो इसका अंकित मूल्य ज्ञात कीजिये |

  1. Rs./रु.800

  2. Rs./रु.1400

  3. Rs./रु.1600

  4. Rs./रु.1800
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Successive discounts: net discount = 30 + 15 - (30×15)/100 = 45 - 4.5 = 40.5%. Customer pays 59.5% of marked price. So 0.595 × MP = 952, giving MP = 952/0.595 = 1600. Option C is correct.

Multiple choice

A man sells an article at a profit of 30%. Had he bought it at 22% less and sold it for Rs.884 less, he would have gained 10%. What is the cost price of the article? एक व्यक्ति एक वस्तु को 30% के लाभ पर बेचता है | यदि वह इसे 22% कम पर खरीदता और इसे 884 रु. कम में बेचता, वह 10% का लाभ प्राप्त करता | वस्तु का क्रय मूल्य क्या है ?

  1. Rs./रु.1400

  2. Rs./रु.1750

  3. Rs./रु.2000

  4. Rs./रु.3000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = x. SP = 1.3x (30% profit). New CP = 0.78x (22% less). New SP = 1.3x - 884. New profit = 10%, so (1.3x - 884)/0.78x = 1.1 → 1.3x - 884 = 0.858x → 0.442x = 884 → x = 884/0.442 = 2000. Option A (1400) and B (1750) are incorrect.

Multiple choice

Two items are sold at a profit of 10% and 15% respectively. If the amount of profit received is same, then what is the cost price of first item, if selling price of second item is Rs.2300? दो वस्तुओं को क्रमशः 10% और 15% के लाभ पर बेचा जाता है | यदि प्राप्त लाभ की धनराशि समान है, तो पहली वस्तु का क्रय मूल्य क्या है, यदि दूसरी वस्तु का विक्रय मूल्य 2300 रु. है ?

  1. Rs./रु.1000

  2. Rs./रु.5000

  3. Rs./रु.4000

  4. Rs./रु.3000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP1 = x and CP2 = y. Profit on first item = 10% of x = 0.10x. Profit on second item = 15% of y = 0.15y. Since profits are equal: 0.10x = 0.15y. Also, SP of second item = y + 0.15y = 1.15y = 2300, so y = 2000. Therefore profit = 0.15 × 2000 = 300. Solving: 0.10x = 300, x = 3000. Hence CP of first item is Rs. 3000.

Multiple choice

A dishonest trader marks up his goods by 80% and gives a discount of 25%. Besides, he cheats 20% while purchasing and 10% while selling. Find the overall profit percentage of shopkeeper.

  1. 60%

  2. 40%

  3. 75%

  4. 80%

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Assuming CP = 100 units. While purchasing, trader gets 120 units for 100 (cheats 20%), so effective CP per unit = 100/120 = 5/6. He marks up by 80%, so MP = 100 × 1.8 = 180. After 25% discount, SP = 180 × 0.75 = 135. While selling, he gives only 90 units but charges for 100 (cheats 10%), so effective SP per unit = 135/0.9 = 150. Profit = 150 - (100/120) × 100 = 150 - 83.33 = 66.67 on CP 83.33, which is 80%.

Multiple choice

On selling 19 articles at Rs. 840, there is a loss equal to the cost price of 5 articles. The cost price of an article is- 19 वस्तुओं को 840 रू. में बेचने पर 5 वस्तुओं के क्रय मूल्य के बराबर हानि हाती है। एक वस्तु का क्रय मूल्य है-

  1. Rs. 55

  2. Rs. 60

  3. Rs. 45

  4. Rs. 50
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let CP of one article = x. Total CP = 19x, Total SP = 840. Loss = CP - SP = 19x - 840 = 5x. So 19x - 840 = 5x, giving 14x = 840, x = 60. CP of each article is Rs. 60.

Multiple choice

On allowing 20% discount, 12% loss is occured. How much the marked price is above the cost price ? 20% छूट देने पर 12% का नुकसान होता है। अंकित मूल्य क्रय मूल्य से कितने प्रतिशत अधिक है ?

  1. 15%

  2. 12%

  3. 10%

  4. 8%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = 100. A 12% loss means SP = 88. Since a 20% discount is given on MP, we have SP = 0.8 × MP. So 0.8 × MP = 88, which gives MP = 110. Therefore, MP is 10% above CP. Alternatively, if selling at 12% loss after 20% discount, then MP/CP = (100 - 12)/(100 - 20) = 88/80 = 1.10, so MP is 10% above CP.

Multiple choice

A man observes that the cost of selling price of certain number of oranges is equal to cost of 125% of that number of oranges bought.Find his profit percent. एक आदमी देखता है कि निश्चित संख्या में बेचे गए संतरों की संख्या का विक्रय मूल्य उस संख्या का 125% संतरों की संख्या के क्रय मूल्य के बराबर है। उसका लाभ प्रतिशत ज्ञात कीजिये।

  1. 15%

  2. 20%

  3. 25%

  4. 10%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the selling price of certain oranges equals the cost price of 125% of that same number, then SP = 125% of CP for equal quantities. This means SP/CP = 125/100 = 5/4. Profit percent = (SP - CP)/CP × 100 = (5-4)/4 × 100 = 25%.

Multiple choice

The difference is selling an article at profits of 4% and 6% is Rs. 12. The cost price of the article is- एक वस्तु का 4% और 6% लाभ पर बेचने का अन्तर 12 रू. है। वस्तु का क्रय मूल्य क्या है?

  1. Rs./रु.500

  2. Rs./रु.575

  3. Rs./रु.600

  4. Rs./रु.625
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Difference in profit = 6% - 4% = 2% of CP. This equals Rs. 12. So 0.02 × CP = 12, CP = 12/0.02 = 600. Option C is correct. Verify: 4% of 600 = 24, 6% of 600 = 36, difference = 12 ✓

Multiple choice

An article was sold at a profit of 12%. If the cost price would be 10% less and selling price would be Rs. 5.75 more, there would be profit of 30%. Then at what price it should be sold to make a profit of 20%? एक वस्तु को 12% लाभ पर बेचा जाता है | यदि क्रय मूल्य 10% कम होता और विक्रय मूल्य 5.75 रु. अधिक होता, तो 30% का लाभ होता | तो 20% का लाभ प्राप्त करने के लिए इसे किस मूल्य पर बेचा जाना होगा ?

  1. Rs./रु.115

  2. Rs./रु.120

  3. Rs./रु.138

  4. Rs./रु.215
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = x. SP = 1.12x. New CP = 0.9x, new SP = 1.12x + 5.75. New profit = 30%, so 1.12x + 5.75 = 1.3(0.9x) = 1.17x. Thus 5.75 = 0.05x, x = 115. For 20% profit: SP = 1.2(115) = 138.

Multiple choice

Some articles are bought at rate of 12 for Rs.20 and equal number of articles are bought at rate of 15 for Rs.12.If each article is sold at rate of Rs.1.60 per article find overall profit/ loos percentage.(Approx)

  1. 39%

  2. 14%

  3. 22%

  4. 30%

  5. 42%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First batch: 12 articles for Rs.20, so CP = 20/12 = Rs.5/3 per article. Second batch: 15 articles for Rs.12, so CP = 12/15 = Rs.4/5 per article. Average CP = (5/3 + 4/5)/2 = (25/15 + 12/15)/2 = (37/15)/2 = Rs.37/30 ≈ Rs.1.233 per article. SP = Rs.1.60 per article. Profit = 1.60 - 1.233 = Rs.0.367 per article. Profit % = (0.367/1.233) × 100 ≈ 29.7%. The options are 39%, 14%, 22%, 30%, 42%. 30% is closest to 29.7%, so option D is correct.

Multiple choice

Ranjan made a profit of 25% when selling a TV set at Rs. 3000. If he now has to pay Rs. 500 more for the set, what should be his new selling price in order to make the same percentage of profit ? रंजन एक टी.वी. सेट को जब 3000 रू. में बेचता है तो 25% का लाभ पाता है यदि वह अब 500 रू.अधिक भुगतान करे तो वही लाभ प्रतिशत के लिए नया विक्रय मूल्य कितना होना चाहिए?

  1. Rs. / रू.3600

  2. Rs./ रू. 3625

  3. Rs./ रू.3650

  4. Rs. / रू.4000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original scenario: Selling price = Rs. 3000, profit = 25%. Cost price = 3000/(1 + 0.25) = 3000/1.25 = Rs. 2400. New cost price = 2400 + 500 = Rs. 2900. To maintain 25% profit: New selling price = 2900 × 1.25 = Rs. 3625.