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

The profit percent earned by selling an article for Rs. 1920 is equal to the loss percent earned by selling the same article for Rs. 1280. At what price should he sell the article so that profit earned is 30%?

  1. Rs.2000

  2. Rs.2400

  3. Rs.2280

  4. Rs.2080

  5. Rs.2580
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Since profit percent at Rs.1920 equals loss percent at Rs.1280, the cost price must be exactly midway: (1920 + 1280) ÷ 2 = Rs.1600. To earn 30% profit, selling price = 1600 × 1.3 = Rs.2080. Option A (Rs.2000) would give a 25% profit, not 30%. Option B (Rs.2400) represents a 50% profit. Option C (Rs.2280) would be approximately 42.5% profit, which doesn't match the requirement.

Multiple choice

In which ratio water is mixed with milk so that by selling mixture at the cost price he may gains 20\%?

  1. 1 : 2

  2. 2 : 3

  3. 5 : 1

  4. 1 : 4

  5. 6 : 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To gain 20% by selling at cost price, 20% of the mixture must be water (free). Let milk be M and water be W. Selling at CP means: CP(M+W) = SP(M+W) = 1.2×CP(M). This gives: CP(M+W) = 1.2×CP(M), so M+W = 1.2M, meaning W = 0.2M. Therefore W:M = 0.2:1 = 1:5, so water:milk = 1:5 ✓

Multiple choice

A trader marked his goods at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. Find his total gain %? एक व्यापारी अपनी वस्तुओं पर क्रय मूल्य से 20% अधिक अंकित करता है। वह आधी वस्तुओं को अंकित मूल्य पर ही बेचता है और चौथाई वस्तुओं को 20% छूट पर और शेष वस्तुओं को 40% छूट पर बेचता है। कुल प्रतिशत लाभ ज्ञात कीजिये ?

  1. 0%

  2. 2%

  3. 5%

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

Let CP = 100. Marked price = 120. Half sold at 120: revenue = 60. Quarter at 20% discount: sells at 96, revenue = 24. Quarter at 40% discount: sells at 72, revenue = 18. Total revenue = 102 on CP of 100. Gain = 2%.

Multiple choice

The percentage of profit, when an article is sold for Rs.78 is twice that when it is sold for Rs.69. The cost price of the article is : किसी वस्तु को 69 रू. में बेचने के बजाय 78 रू. में बेचने पर लाभ की प्रतिशतता दुगुनी है । उस वस्तु का क्रय मूल्य है-

  1. 55

  2. 59

  3. 60

  4. 65
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let cost price be C. When sold for Rs.69, profit percent equals (69 minus C) over C times 100. When sold for Rs.78, profit percent equals (78 minus C) over C times 100. Given that (78 minus C) over C equals 2 times (69 minus C) over C. Solving gives 78 minus C equals 2 times (69 minus C), so 78 minus C equals 138 minus 2C, giving C equals 60.

Multiple choice

A person bought 50 pens for Rs. 50 each. He sold 40 of them at a loss of 5%. He wants to gain 10% on the whole. Then his gain percent on the remaining pens should be - एक व्यक्ति ने 50 पेन 50 रू. प्रति पेन की दर से खरीदे। उसने 40 पेन 5% हानि पर बेच दिये। अब वह अगर 10% कुल लाभ का आकांक्षी हो, तो उसे शेष पेन कितने प्रतिशत लाभ पर बेचने होंगे?

  1. 15

  2. 40

  3. 50

  4. 70
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Cost = 50 × 50 = 2500. Desired profit = 10% of 2500 = 250. Target amount = 2750. Sold 40 pens at 5% loss: 40 × 50 × 0.95 = 1900. Remaining 10 pens must sell for: 2750 - 1900 = 850. Per pen = 85. Profit per remaining pen = 85 - 50 = 35. Profit % = 35/50 × 100 = 70%.

Multiple choice

After allowing a discount of 16%, there was still a gain of 5%. The the percentage of marked price over the cost price is- किसी वस्तु पर 16% छूट देने पर भी 5% का लाभ प्राप्त हो जाता है। तो उस वस्तु का अंकित मूल्य उसके लागत मूल्य से कितने प्रतिशत अधिक है?

  1. 15%

  2. 18%

  3. 21%

  4. 25%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let cost price = 100. Selling price after 5% profit = 105. This selling price is obtained after 16% discount on marked price, so SP = MP × (1 - 16/100) = MP × 0.84. Therefore MP = 105/0.84 = 125. Marked price exceeds cost price by 125 - 100 = 25%.

Multiple choice

A shopkeeper makes a profit of 10% on selling an article. What will be the percentage change in the profit percent if he had buy it for 20% less and sold it for 10% more? एक दुकानदार को किसी वस्तु को बेचने पर 10% का लाभ होता हैं | लाभ प्रतिशत में कितने प्रतिशत का बदलाव आयगा यदि वह वास्तु को 20% कम पर खरीद कर 10% अधिक पर बेच दे ?

  1. 41.25%

  2. 51.25%

  3. 412.5%

  4. 512.5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = 100, SP = 110 (10% profit). New scenario: CP = 80 (20% less), SP = 121 (10% more on 110). New profit = 121 - 80 = 41. New profit percent = 41/80 × 100 = 51.25%. Original profit = 10%. Percentage change = ((51.25 - 10)/10) × 100 = 412.5%. This asks for change IN the profit percent, not the change in profit amount. Option A is the new profit percent, not the change. Option B and D are distractors.

Multiple choice

A trader sells two cycles at Rs 1,188 each and gains 10% on the first and loss 10% on the second.What is the profit or loss percent on the whole? एक व्यापारी दो साइकिलें प्रत्येक 1,188 में बेचता है और पहली पर 10% का लाभ तथा दूसरी पर 10% की हानि उठाता है। कुल पर लाभ या हानि का प्रतिशत कितना है?

  1. 1% loss/हानि

  2. 1% gain/लाभ

  3. No loss no gain/न हानि न लाभ

  4. 2% loss/हानि
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When same selling price with x% gain and x% loss, there is always x^2/100% loss overall. Here x=10, so loss = 100/100 = 1%. Option B is correct. Alternatively: For first cycle, CP = 1188/1.1 = 1080. For second, CP = 1188/0.9 = 1320. Total CP = 2400, total SP = 2376, loss = 24/2400 = 1%.

Multiple choice

A person bought an article on 40% discount and sold it at 50% more that the marked price find his profit %. एक व्यक्ति 40% छूट पर एक वस्तु खरीदता है और उसे अंकित मूल्य से 50% अधिक पर बेचता है तो उसका लाभ % ज्ञात कीजिए।

  1. 160%

  2. 150%

  3. 90%

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

Let marked price = M. Buying price after 40% discount = 0.6M. Selling price at 50% above marked price = 1.5M. Profit = 1.5M - 0.6M = 0.9M. Profit% = (0.9M/0.6M) × 100 = 150%. Option C (90%) would result from calculating profit on marked price instead of cost price.

Multiple choice

The cost price of 20 oranges is same with selling price of 16 oranges. The profit percentage is 20 संतरों का लागत मूल्य 16 संतरों के बिक्री मूल्य के बराबर है। तद्नुसार उन पर प्राप्त लाभ प्रतिशत ज्ञात कीजिए।

  1. 16%

  2. 20%

  3. 25%

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

Let CP of 1 orange = x. SP of 1 orange = 20x/16 = 1.25x. Profit = SP - CP = 0.25x. Profit % = (0.25x/x) × 100 = 25%. Alternatively, using the formula: Profit% = ((20-16)/16) × 100 = 25%.

Multiple choice

On selling an article at 2/3 of the marked price, the loss is 10%. If the article is sold at marked price what will be profit percent ?

  1. 20%

  2. 30%

  3. 35%

  4. 40%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = cost price, MP = marked price. Selling at 2/3 MP gives 10% loss: (2/3)MP = 0.9CP, so MP = 1.35CP. At MP, profit = MP - CP = 1.35CP - CP = 0.35CP = 35%. Option A (20%) is incorrect; it would only apply if the relationship between MP and CP was different.

Multiple choice

A man sold an article at a loss of 4%. Had he sold it at a gain of 12%, it would have feteched Rs. 132 more than it did. What was the cost price? एक आदमी एक वस्तु को 4% हानि पर बेचता है। यदि वह इससे 12% लाभ पर बेचे तो वह इससे 132 रू. अधिक प्राप्त करता है। वस्तु का क्रय मूल्य क्या था?

  1. Rs. 1000

  2. Rs. 825

  3. Rs. 1650

  4. Rs. 1100
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The difference between 12% gain and 4% loss is 16% of CP. This 16% equals Rs. 132. So CP = 132/0.16 = Rs. 825. Verification: 4% loss gives 825×0.96 = Rs. 792; 12% gain gives 825×1.12 = Rs. 924; difference = Rs. 132.

Multiple choice

The marked price of a mixie is Rs. 1600. The shopkeeper gives successive discount of 10% and x% to the customer. If the customer pays Rs. 1224 for the mixie, find the value of x एक मिक्सी का अंकित मूल्य रू. 1600 है। उस पर दुकानदार अपने खरीदार को 10% तथा x% की क्रमिक छूटें देता है। तदनुसार, यदि खरीदार ने उस मिक्सी के 1224 रू. दिए हों, तो x का मान ज्ञात कीजिए।

  1. 12 %

  2. 15 %

  3. 8 %

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

After first discount of 10%: 1600 × 0.9 = 1440. After second discount of x%: 1440 × (1 - x/100) = 1224. Solving: 1 - x/100 = 1224/1440 = 0.85, so x/100 = 0.15, meaning x = 15%. For successive discounts, apply them sequentially - you can't just add the percentages.

Multiple choice

A shopkeeper marks the price of an article at Rs. 80. What will be the selling price, if he allows two successive discounts at 5 % each? एक दुकानदार एक वस्तु का मूल्य 80 रू. अंकित करता है। तदनुसार, यदि वह उसे प्रत्येक 5% की दो क्रमिक छूटें देकर बेचे, तो उसका विक्रय मूल्य कितना होगा?

  1. Rs. 72

  2. Rs. 85

  3. Rs. 7.2

  4. Rs. 72.2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Marked price = Rs. 80. After first 5% discount: 80 × 0.95 = Rs. 76. After second 5% discount: 76 × 0.95 = Rs. 72.20. For successive discounts, multiply the factors: (1 - 0.05)(1 - 0.05) = 0.9025, so 80 × 0.9025 = 72.20. Don't make the error of simply subtracting 10% from 80.

Multiple choice

A person has a loss of 4% on selling 4 articles in Rs.1. If he sold 3 articles in one rupee, then what percent profit he obtained? 1 रु. में 4 वस्तुएं बेचकर एक आदमी को 4% की हानि होती है | यदि उसने 1 रु. में 3 वस्तुएं बेची होती तो उसे कितने प्रतिशत का लाभ होता ?

  1. 12%

  2. 30%

  3. 28%

  4. 16%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Selling 4 articles for Rs.1 means SP = 25 paise per article. With 4% loss: CP = SP/(1-0.04) = 25/0.96 ≈ 26.04 paise. If 3 articles are sold for Rs.1, new SP = 100/3 ≈ 33.33 paise. Profit = 33.33 - 26.04 = 7.29 paise. Profit percent = (7.29/26.04) × 100 ≈ 28%.