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

Rajesh purchased two bicycles and sold them at equal selling price. On first cycle he got a profit of 40% and on second cycle he got a profit of 25%. Find that cost price of costlier cycle is how much percent more than the price of cheaper cycle?

  1. 22.5%

  2. 25%

  3. 20%

  4. 42%

  5. 12%
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let SP be the selling price for both cycles. CP1 = SP/1.4, CP2 = SP/1.25. The costlier cycle is the one with higher CP. CP1 = 0.714SP, CP2 = 0.8SP. So cycle 2 is costlier. Difference = 0.8SP - 0.714SP = 0.086SP. Percentage more = (0.086SP / 0.714SP) × 100 = 12.04%. The costlier cycle is approximately 12% more expensive than the cheaper one.

Multiple choice

A shopkeeper has a weighing machine which shows 1 kg. as 1200 gm. He marks up the goods 10% above the cost price then net profit percent is- /एक दुकानदार के पास एक तराजू है जो एक किग्रा. के स्थान पर 1200 ग्राम दिखाता है। वह अपने क्रय मूल्य पर भी 10 प्रतिशत अधिक अंकित करता है तो शुद्ध लाभ प्रतिशत है-

  1. 32%

  2. 23%

  3. 31.75%

  4. 23.5%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The shopkeeper gives only 1000 gm instead of 1200 gm shown, so effective quantity = 1000/1200 = 5/6 of paid quantity. With 10% markup, selling price = 1.10 × cost per kg. Effective selling price for actual quantity = 1.10 / (5/6) = 1.10 × 1.2 = 1.32. Net profit = 32%.

Multiple choice

A man sells two horses for Rs. 1485. The cost price of the first is equal to the selling price of the second. If the first is sold at 20% loss and the second at 25% gain, what is his total gain or loss (in rupees)?

  1. Rs. 80 gain

  2. Rs. 60 gain

  3. Rs. 60 loss

  4. Neither gain nor loss
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP1 = CP2 = x. SP1 = 0.8x (20% loss), SP2 = 1.25x (25% gain). Total SP = 0.8x + 1.25x = 2.05x. Total CP = x + x = 2x. Profit = 0.05x. But given total SP = 1485, so 2.05x = 1485, x = 724.39. Total CP = 2x = 1485 (approximately). Hence no gain no loss.

Multiple choice

Rajesh sold an article to Sachin at a loss of 28%. Sachin spent Rs. 168 on its repairs and sold it to Vijay for Rs. 3591, there by, making a profit of 12.5%. Find the cost price of the article for Rajesh. राजेश, सचिन को एक वस्तु 28% की हानि पर बेचता है। सचिन इसकी मरम्मत पर 168 रू. खर्च करता है और वस्तु को 12.5% लाभ पर विजय को 3591 रू. में बेच देता है। राजेश के लिए क्रय मूल्य ज्ञात कीजिए।

  1. Rs. 3800

  2. Rs. 3500

  3. Rs. 4000

  4. Rs. 4200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work backwards from Vijay's buying price. Sachin sold at 12.5% profit for Rs. 3591, so his cost (including repairs) = 3591/1.125 = 3192. Subtracting Rs. 168 repairs gives Sachin's purchase cost = Rs. 3024. Rajesh sold at 28% loss, so his cost price = 3024/0.72 = Rs. 4200.

Multiple choice

How much percent more than the cost price should a trader mark his goods so that after allowing a discount of 40% on the marked price, he gains 20% ? एक विक्रेता अपने वस्तु के क्रय मूल्य से कितने प्रतिशत अधिक मूल्य अंकित करे कि उसे 40% की छूट देने के पश्चात् वह 20% का लाभ प्राप्त करता है ?

  1. 300%

  2. 100%

  3. 60%

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

Let CP = 100. After gaining 20%, SP = 120. This SP is after 40% discount on MP, so 120 = 0.6*MP, giving MP = 200. Mark-up = (200-100)/100 = 100%. The trader should mark goods 100% above cost price.

Multiple choice

A shopkeeper gives two successive discounts of 30% and 12.5% and finally sells an article for Rs. 245. Find the marked price of the article./एक दुकानदार ने एक वस्तु पर क्रमशः 30% तथा 12.5% की दो क्रमागत छूट दी तथा अन्त में वस्तु को 245 रूपये में बेचा। वस्तु का अंकित मूल्य ज्ञात कीजिए।

  1. Rs. 380

  2. Rs. 400

  3. Rs. 350

  4. Rs. 420
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

After 30% discount, price becomes 70% of marked price. After additional 12.5% (which is 1/8), the remaining is 7/8 of 70% = 61.25%. So 61.25% of MP = 245, meaning MP = 245/0.6125 = 400. Working backwards: 245 ÷ 0.875 = 280, then 280 ÷ 0.7 = 400.

Multiple choice

A person bought 76 cows and sold 20 cows at 15% profit, 40 cows at 19% profit and remaining 16 cows at 25% profit and got a profit of Rs. 6570 as a whole. The cost price of each cow is-

  1. Rs. 450

  2. Rs. 425

  3. Rs. 420

  4. Rs. 400
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let CP = x. Total profit = 20×0.15x + 40×0.19x + 16×0.25x = 3x + 7.6x + 4x = 14.6x. Given profit = Rs. 6570, so 14.6x = 6570, x = 6570/14.6 = Rs. 450. Verification: 20 cows → Rs. 1350 profit, 40 cows → Rs. 3040 profit, 16 cows → Rs. 1800 profit. Total = Rs. 6570.

Multiple choice

An article was sold at a profit of 12%. If the cost price would be 10% less, selling price would be 6.75 more, there would be a profit of 30%. Then what is the cost price of the article? /एक वस्तु 12 प्रतिशत के लाभ पर बेची जाती है। यदि क्रय मूल्य 10 प्रतिशत कम हो और विक्रय मूल्य रू. 6.75 अधिक हो, तो 30 प्रतिशत का लाभ होगा। तो वस्तु का क्रय मूल्य क्या है?

  1. Rs. 115

  2. Rs. 135

  3. Rs. 125

  4. Rs.145
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let CP = x. Original: SP = 1.12x. New CP = 0.90x, New SP = 1.12x + 6.75, Profit = 30%. So (1.12x + 6.75)/(0.90x) = 1.30. 1.12x + 6.75 = 1.17x. 6.75 = 0.05x. x = 6.75/0.05 = 135. Therefore CP = Rs. 135. This is verified by checking: Original SP = 135 × 1.12 = 151.20. New CP = 121.50, New SP = 151.20 + 6.75 = 157.95. Profit = (157.95 - 121.50)/121.50 = 36.45/121.50 = 0.30 = 30%. ✓

Multiple choice

A person sells an article at a profit of 10%. If he had bought the article at 5% less cost and sold for Rs. 8 more, he would have gained 20%. The cost price of the article is- एक व्यक्ति एक वस्तु को 10% के लाभ पर बेचता है। यदि वह इस वस्तु को 5% कम मूल्य पर खरीदता है और इसे 8 रू. अधिक में बेचता, वह 20% का लाभ प्राप्त करता। वस्तु का क्रय मूल्य है-

  1. 300

  2. 250

  3. 200

  4. 240
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = x. First case: SP at 10% profit = 1.1x. Second case: New CP = 0.95x, new SP = 1.1x + 8, profit = 20%. So 1.2(0.95x) = 1.1x + 8. Solving: 1.14x - 1.1x = 8, so 0.04x = 8, x = 200. Verify: Original CP 200, SP 220. New CP 190, SP 228 = 1.2 × 190 ✓

Multiple choice

If profit percent is 170% of the cost price. If cost price is increased by 50%. Then what will be the profit percent ? यदि लाभ प्रतिशत क्रय मूल्य का 170% है। यदि क्रय मूल्य में 50% की वृद्धि की जाती है तो लाभ प्रतिशत क्या होगा ?

  1. 125%

  2. 80%

  3. 100%

  4. 150%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given: Profit% = 170% of CP. Let CP = 100, then Profit = 170, so SP = 270. If CP increases by 50%, new CP = 150. Assuming same SP = 270, new Profit% = (270-150)/150 × 100 = 120/150 × 100 = 80%. Options A, C, D are incorrect.

Multiple choice

A shopkeeper sells an item at 12.5 profit and also uses a false weight of 1100 grams instead of 1200 grams. Find his overall profit percentage

  1. 18.75%

  2. 19.25%

  3. 21.45%

  4. 22.72%

  5. 22.75%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Shopkeeper earns 12.5% profit on marked price. Additionally, he gives only 1100g instead of 1200g, gaining an extra 100g on every 1100g sold, which is (100/1100) × 100 = 9.09% profit. Total profit = (1 + 12.5/100) × (1 + 9.09/100) - 1 = 1.125 × 1.0909 - 1 = 1.2272 - 1 = 22.72%. Alternatively, using the formula: (Profit% + False gain% + (Profit% × False gain%)/100) = 12.5 + 9.09 + (12.5×9.09)/100 = 22.72%.

Multiple choice

An article is sold at 23% discount for Rs. 1848. What is its marked price? एक वस्तु को 23% की छूट देने के बाद 1848 रू. में बेचा गया। वस्तु का अंकित मूल्य क्या है?

  1. Rs. 2400

  2. Rs. 2600

  3. Rs. 2000

  4. Rs. 2800
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Selling price after 23% discount = 77% of marked price. So 0.77 × MP = 1848. Therefore MP = 1848/0.77 = 2400.

Multiple choice

Aniruddha sold a bicycle at a gain of 8%. If he would sold it for Rs.75 more, the gain would have been 14%, what was the cost price of the bicycle? अनिरूद्ध ने एक साइकिल 8% लाभ पर बेचा, यदि वह इसे रू 75 अधिक में बेचता है तो उसे 14% लाभ होता। साइकिल का क्रय मूल्य क्या था?

  1. Rs.1200

  2. Rs.1250

  3. Rs.1350

  4. Rs.1500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let CP be x. 8% gain means SP = 1.08x. 14% gain means SP = 1.14x. Difference is Rs. 75, so 1.14x - 1.08x = 75, which gives 0.06x = 75, hence x = 75/0.06 = Rs. 1250. The key is recognizing that the additional Rs. 75 represents the difference between 14% and 8% (which is 6%) of the cost price.

Multiple choice

On selling 144 articles, James lost the selling price of 6 articles. His percent loss is- 144 वस्तुओं को बेचने पर जेम्स को 6 वस्तुओं के विक्रय मूल्य के बराबर हानि होती है। उसकी प्रतिशत हानि है -

  1. 4%

  2. 6%

  3. 8%

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

When 144 articles are sold and loss equals SP of 6 articles: Loss = 6 × SP. Loss% = (Loss/CP) × 100. Let CP of 1 article = x, SP of 1 article = y. CP of 144 articles = 144x, SP of 144 articles = 144y. Loss = 144x - 144y = 6y, so 144x = 150y, x/y = 150/144 = 25/24. Loss% = (6y)/(144x) × 100 = (6/144) × (24/25) × 100 = 4%. Alternatively: SP of 144 items loses SP of 6 items, so CP of 144 items = SP of 150 items, ratio CP:SP = 150:144 = 25:24, loss% = (25-24)/25 × 100 = 4%.

Multiple choice

A shopkeeper find his profit as 20% of the selling price. His actual profit percent is- एक दुकानदार विक्रय मूल्य पर 20% लाभ प्राप्त करता है। उसका वास्तविक लाभ प्रतिशत है-

  1. 20%

  2. 22%

  3. 25%

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

If profit is 20% of SP, let SP = 100. Then profit = 20, so CP = 80. Actual profit % = (profit/CP) × 100 = (20/80) × 100 = 25%. The profit percentage is always on cost price, not selling price.