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

In what proportion must water be mixed with milk to gain 60% by selling it at 20% above cost price? दूध में पानी किस अनुपात में मिलाया जाय ताकि मिश्रण को क्रय मूल्य पर 60% बढ़कर बेचने पर 50% का लाभ हो?

  1. 1 : 4

  2. 4 : 1

  3. 1 : 3

  4. 3 : 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let milk cost 1/liter. Water costs 0. Need 60% profit selling at 1.2. So cost of mix = 1.2/1.6 = 0.75. Using alligation: milk at 1, water at 0, mean 0.75 gives ratio 0.75:0.25 = 3:1 (water:milk). So water:milk = 1:3. Option C is correct.

Multiple choice

Two items I and II are sold at a profit of 10% and 15% respectively. If the amount of profit received is the same and that is equal to Rs.300, then the ratio between the cost price of I article and II article is

  1. 2 : 3

  2. 2 : 5

  3. 5 : 2

  4. 3 : 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For item I: CP_I × 0.10 = 300, so CP_I = 3000. For item II: CP_II × 0.15 = 300, so CP_II = 2000. Ratio CP_I : CP_II = 3000 : 2000 = 3 : 2. The key insight is that when profit amounts are equal, the cost prices are inversely proportional to profit percentages.

Multiple choice

By selling an article for Rs. 2850, a shopkeeper gains 14%. If he marked the price of the article 35% above of the cost price and then gives a discount of 20%, then profit is reduced to x%, then the selling price will be एक वस्तु को 2850 रु. में बेचकर, एक दुकानदार 14% का लाभ प्राप्त करता है | यदि वह वस्तु को उसके क्रय मूल्य से 35% अधिक मूल्य पर अंकित करता है और फिर 20% की छूट भी देता है, तो लाभ घटकर x% हो जाता है, तो विक्रय मूल्य होगा

  1. Rs./रु.2600

  2. Rs./रु.2700

  3. Rs./रु.2800

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

SP at 14% profit = 2850, so CP = 2850/1.14 = 2500. Marked price = 2500 × 1.35 = 3375. After 20% discount, new SP = 3375 × 0.8 = 2700. Option B matches exactly. The profit at this SP is (2700-2500)/2500 = 8%.

Multiple choice

A person sold a novel at a gain of 20%. Had he bought it for 40% less and sold it for Rs.1350 less, he would have made a profit of 40%. The cost price of the novel was: एक व्यक्ति एक उपन्यास की किताब को 20% लाभ पर बेचता है | यदि वह इसे 40% कम मूल्य पर खरीदता और 1350 रु. कम में बेचता, वह 40% का लाभ प्राप्त करता| उपन्यास का क्रय मूल्य था :

  1. Rs./रु.2750

  2. Rs./रु.2250

  3. Rs./रु.3250

  4. Rs./रु.3750
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP = x. At 20% profit, SP = 1.2x. If CP = 0.6x (40% less) and sold for (1.2x - 1350), profit is 40% on reduced CP, so 1.4 × 0.6x = 1.2x - 1350 → 0.84x = 1.2x - 1350 → 0.36x = 1350 → x = 3750. Option D is correct.

Multiple choice

A shopkeeper sold an article at a loss of 25%.If the selling price had been increased by Rs.210, there would have been a gain of 10%. The cost price of the article (in Rs.) was - एक व्यापारी ने एक वस्तु 25% हानि पर बेची। यदि उसने उसका विक्रय मूल्य 210 रू. बढ़ा दिया होता, तो उसे 10% लाभ मिलता। तदनुसार, उस वस्तु का लागत मूल्य (रूपयें में) था-

  1. Rs./रु. 300

  2. Rs./रु.450

  3. Rs./रु.575

  4. Rs./रु.600
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP = x. Selling at 25% loss means SP = 0.75x. Increasing SP by 210 gives 0.75x + 210 = 1.1x (for 10% gain). Solving: 210 = 0.35x, so x = 600. The Rs.210 increase bridges the gap from 25% loss to 10% gain, which is a 35% swing in CP.

Multiple choice

A merchant fixed the selling price of his articles at Rs. 1400 after adding 40% profit to the cost price. As the sale was very low at this price, he decided to fix the selling price at 15% profit. Find the difference between old selling price and new selling price. क्रय मूल्य पर 40 प्रतिशत लाभ जोड़ते हुए एक व्यापारी अपनी वस्तु की कीमत 1400 रू. निर्धारित करता है। चूँकि बिक्री बहुत कम थी अतः वह अब क्रय मूल्य पर 15 प्रतिशत लाभ हेतु विक्रय मूल्य निर्धारित करता है। नये और पुराने विक्रय मूल्य के बीच का अंतर ज्ञात कीजिए।

  1. 150

  2. 200

  3. 250

  4. 300
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Selling price at 40% profit = 1400, so cost price = 1400/1.4 = 1000. New selling price at 15% profit = 1000 × 1.15 = 1150. Difference = 1400 - 1150 = 250.

Multiple choice

A man sold two articles at the same price. He obtained 20% profit on first article and 25% profit on second article. If the cost price of the first article is Rs.100, then find the cost price of the second article. एक आदमी दो वस्तुओं को समान मूल्य पर बेचता है | वह पहली वस्तु पर 20% का लाभ और दूसरी वस्तु पर 25% का लाभ प्राप्त करता है | यदि पहली वस्तु का क्रय मूल्य 100 रु. है, तो दूसरी वस्तु का क्रय मूल्य ज्ञात कीजिये |

  1. Rs./रु.100

  2. Rs./रु.96

  3. Rs./रु.90

  4. Rs./रु.105
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Selling price of first article: 100 × 1.20 = 120. Let CP of second article = x. Selling price: x × 1.25 = 120. Solving: x = 120/1.25 = 96. Equal selling prices mean the 25% profit on the second must give the same final amount as 20% profit on the first.

Multiple choice

On selling 144 articles a man lost amount equal to selling price of 6 articles. Then what is the percentage of loss? 144 वस्तुओं को बेचने पर एक व्यक्ति को 6 वस्तुओं के विक्रय मूल्य के बराबर हानि हुई | तदनुसार उसके घाटे का प्रतिशत कितना है ?

  1. 4

  2. 5

  3. 3

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let SP = selling price per article. Loss = 144(CP - SP) = 6SP, so 144CP = 150SP, meaning CP/SP = 150/144 = 25/24. Loss per article = CP - SP = 25 - 24 = 1 unit on CP of 25. Loss percentage = (1/25) × 100 = 4%. The loss of 6 articles' SP is distributed across 144 articles sold.

Multiple choice

With a 5% discount on the cost of sugar, a buyer could purchase 2 kg more sugar for Rs. 608. What is the selling price of sugar? चीनी के मूल्य पर 5% छूट देने पर एक खरीददार 608 रू. में 2 किग्रा चीनी अधिक खरीद सकता है। चीनी का विक्रय मूल्य क्या है?

  1. Rs. 15.50

  2. Rs. 15

  3. Rs. 16.50

  4. Rs. 16
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the original price per kg be P. With 5% discount, the discounted price is 0.95P. For Rs. 608, original quantity = 608/P kg, discounted quantity = 608/(0.95P) kg. The difference is 2 kg more with discount, so: 608/(0.95P) - 608/P = 2. Solving: 608/P × (1/0.95 - 1) = 2, which gives 608/P × 0.05/0.95 = 2, so P = 608 × 0.05 / (2 × 0.95) = 16. The original (selling) price is Rs. 16/kg.

Multiple choice

A man sells a T.V. set for Rs. 3450 and makes a profit of 15%. He sells a second T.V. set at a loss of 10%. If on the whole he neither gains nor loses, find the cost price of the second T.V. set. एक आदमी एक टी.वी. रू.3450 में बेचता है और 15% का लाभ पाता है। वह दूसरी टी.वी. 10% हानि पर बेचता है। यदि सम्पूर्ण में न तो लाभ और न ही हानि होती है तो दूसरी टी.वी. का क्रय मूल्य ज्ञात कीजिए।

  1. Rs. 3450

  2. Rs. 4500

  3. Rs. 3018

  4. Rs. 2016
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First TV: SP = Rs. 3450, profit = 15%, so CP = 3450 ÷ 1.15 = Rs. 3000, profit = Rs. 450. For no overall profit/loss, second TV must have loss of Rs. 450 at 10%. If loss is 10% of CP₂ = 450, then CP₂ = 450 ÷ 0.10 = Rs. 4500. Option A equals first TV's SP, option C assumes 10% of 3450, and option D miscalculates the base.

Multiple choice

A sofa-set listed at Rs. 800 is sold to a retailer at successive discount of 25% and 15% by the wholesealer. Then the cost price of the sofa-set for retailer is - एक सोफा-सेट का सूचित मूल्य 800 रू. है, को थोक विक्रेता द्वारा, फुटकर विक्रेता को 25% और 15% की क्रमिक छूटों पर बेचा जाता है, तो फुटकर विक्रेता के लिए सोफा सेट का क्रय मूल्य क्या है?

  1. Rs. 500

  2. Rs. 510

  3. Rs. 550

  4. Rs. 560
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First discount 25%: Price = 800 × 0.75 = Rs. 600. Second discount 15%: Final = 600 × 0.85 = Rs. 510. Successive discounts multiply, they don't add up.

Multiple choice

A shopkeeper sold two articles, one at a gain of 20% and the other at a loss of 20%. If the selling price of both were the same, how much percent did he gain or loss on the whole? एक दुकानदार दो वस्तुओं, एक को 20 प्रतिशत लाभ पर तथा दूसरी को 20 प्रतिशत हानि पर बेचता हैं। यदि दोनों का विक्रय मूल्य समान हो, तो सम्पूर्ण पर उसे कितना लाभ या हानि प्राप्त हुई?

  1. 4% gain/लाभ

  2. 4% loss/हानि

  3. No loss or gain/कोई हानि या लाभ नही

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

When selling two items at the same SP with one at 20% gain and another at 20% loss, the net outcome is always a loss. The loss amount (based on higher CP) is always greater than the profit amount (based on lower CP). For equal SPs, the net loss percentage is (20/2)² = 4%. Here: if SP = 120, CP1 = 100; if SP = 80, CP2 = 100. Total CP = 200, total SP = 200, which initially seems balanced, but the actual calculation shows 4% overall loss.

Multiple choice

A shopkeeper marks an article at Rs. 60 and sells it at a discount of 15%. He also gives a gift worth Rs. 3. If he still makes 20% profit, the cost price, in rupees, is एक दुकानदार एक वस्तु को 60 रु. में अंकित करता है और इसे 15% की एक छूट पर बेचता है | वह 3 रु. की कीमत वाला उपहार भी देता है | यदि वह अभी भी 20% का लाभ प्राप्त करता है, क्रय मूल्य, रुपये में, है

  1. 20

  2. 32

  3. 40

  4. 42
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Marked price Rs. 60 with 15% discount gives SP = Rs. 60 × 0.85 = Rs. 51. After deducting the gift worth Rs. 3, effective SP = Rs. 51 - Rs. 3 = Rs. 48. For 20% profit: CP × 1.2 = Rs. 48, so CP = Rs. 40. Option A (Rs. 20) would imply 140% profit. Option B (Rs. 32) gives 50% profit.

Multiple choice

A trader purchased a gift box for Rs.150. What should be the marked price on the gift box so that after allowing a discount of 10%, he makes a profit of 10%? एक विक्रेता एक गिफ्ट बॉक्स 150 रु. में खरीदता है | गिफ्ट बॉक्स को किस मूल्य पर पर अंकित किया जाना चाहिए ताकि 10% की एक छूट देने के बाद भी वह, 10% का लाभ प्राप्त कर सके ?

  1. Rs.180

  2. Rs.183.3

  3. Rs.186.6

  4. Rs.190
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

CP = Rs. 150. Desired profit = 10%, so target SP = Rs. 165. After 10% discount, MP × 0.9 = 165, so MP = 165/0.9 = Rs. 183.33 (approx). This matches option B.

Multiple choice

A trader bought two mobiles for Rs. 39000. He sold one at a loss of 20% and the other at a profit of 15%. If selling price of each mobile is the same, then their cost price are respectively.

  1. 20,000 & 19000

  2. 1000 & 18000

  3. 22000 & 17000

  4. 23000 & 16000

  5. 24000 & 15000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let cost prices be x and y with x + y = 39000. Selling at 15% profit: 1.15x. Selling at 20% loss: 0.8y. Since selling prices are equal: 1.15x = 0.8y, so y = (1.15/0.8)x = 1.4375x. Substituting: x + 1.4375x = 39000, so 2.4375x = 39000, x = 16000. Then y = 23000. The cost prices are Rs. 23000 and Rs. 16000 respectively. Therefore, option D is correct.