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

An article is marked 25% above its cost price. If (x)% discount is allowed on the marked price and still there is a profit of 5.5%, then what is the value of (x)?

  1. 15.6

  2. 15.4

  3. 15.2

  4. 15.3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let cost price = 100. Marked price = 125 (25% above cost). After x% discount, selling price = 125(1 - x/100). Profit = 5.5%, so selling price = 105.5. Therefore 125(1 - x/100) = 105.5, giving 1 - x/100 = 0.844, so x/100 = 0.156, and x = 15.6. The discount brings the marked price down to achieve the desired profit margin.

Multiple choice

A shopkeeper marks his goods 30% higher than the cost price and allows a discount of 10% on the marked price. In order to earn 6.5% more profit, what discount percent should he allow on the marked price?

  1. 5

  2. 4

  3. 6.5

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

Let CP = 100. Marked price = 130, selling price after 10% discount = 117. Current profit = 17%. For 6.5% more profit (total 23.5%), SP should be 123.5. Discount = 130 - 123.5 = 6.5, which is 6.5/130 × 100 = 5%. The profit increases when discount decreases.

Multiple choice

The marked price of an article is Rs.1,280. If a shopkeeper sold the article at 12% profit after giving 30% discount, then the cost price of the article is:

  1. 850

  2. 700

  3. 750

  4. 800
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Selling price = 1280 × 0.70 (after 30% discount) = 896. Since this is 12% profit, Cost Price = 896/1.12 = 800. The solution flow is: Marked Price → Discount → Selling Price → Profit % → Cost Price. Many students mistakenly try to apply percentages directly to the marked price.

Multiple choice

Five percent more is gained by selling an article for Rs 190 than by selling it for Rs 180. Find its cost price.

  1. Rs 200

  2. Rs 205

  3. Rs 195

  4. Rs 210
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The profit percentage increases by 5 percentage points when selling price increases from Rs 180 to Rs 190. Let CP be x. Then (190-x)/x - (180-x)/x = 5/100, which gives 10/x = 0.05, so x = 200. The cost price is Rs 200. Option D (Rs 210) would give profits of 5% and 8.3% respectively - a difference of only 3.3 percentage points, not 5%.

Multiple choice

A trader bought two articles for Rs.490. He sold one at a loss of 20% and the other at a profit of 16%. If the selling price of both articles is the same, then the cost price (in Rs.) of the article sold at 20% loss is:

  1. 300

  2. 280

  3. 310

  4. 290
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CPs be x and y. SP1 = 0.8x, SP2 = 1.16y. Since SP1 = SP2: 0.8x = 1.16y, so y = (0.8/1.16)x. Total: x + (0.8/1.16)x = 490. x(1 + 0.8/1.16) = 490. x = 490 × 1.16/1.96 = 290.

Multiple choice

A shopkeeper allows 16% discount on every item. Even after giving the discount, he makes a profit of 8%. If he gives 8% discount instead of 16% on an item marked for Rs.1800, then what will be his profit percent? (correct to 2 decimal places)
  1. $19$
  2. $18$
  3. $18.31$
  4. $18.29$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

With 16% discount: SP = 0.84MP = 1.08CP, so CP = 0.84/1.08 × MP. For MP = 1800: CP = 0.84/1.08 × 1800 = 1400. With 8% discount: SP = 0.92 × 1800 = 1656. Profit = (1656-1400)/1400 × 100 = 18.29%.

Multiple choice

The marked price of an article is Rs. 240. A shopkeeper sells it by allowing 18% discount on its marked price and still gains 23%. What is the cost price (in Rs.) of the article?

  1. 160

  2. 180

  3. 200

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

Marked Price = Rs. 240. Discount = 18%, so Selling Price = 240 × (1 - 0.18) = 240 × 0.82 = Rs. 196.80. Profit = 23%, so Cost Price = Selling Price / (1 + profit%) = 196.80 / 1.23 = Rs. 160. Verification: 23% of 160 = 36.80, 160 + 36.80 = 196.80 ✓

Multiple choice

The marked price of an article is Rs. 1500. A shopkeeper sells it by giving 20% discount on its marked price. If the cost price of the article is Rs. 991, then his profit (in Rs.) is:

  1. 209

  2. 189

  3. 319

  4. 199
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Selling price after 20% discount on Rs. 1500 = 1500 - (20/100 × 1500) = 1500 - 300 = Rs. 1200. Profit = Selling Price - Cost Price = 1200 - 991 = Rs. 209. The key is to first calculate the selling price after discount, then subtract cost price to find profit.

Multiple choice

The selling price of an article marked for Rs. 10000 after giving three discounts, 20%, 10% and k% is Rs. 6120. What will be selling price (in Rs.) of the same article if a single discount of (k + 20)% is allowed?

  1. 6500

  2. 8000

  3. 8500

  4. 6800
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

After 20% discount: 10000 × 0.8 = 8000. After 10% discount: 8000 × 0.9 = 7200. After k% discount to reach 6120: 6120 = 7200(1 - k/100), giving k = 15%. Single discount of (15 + 20)% = 35% on Rs. 10000: 10000 × 0.65 = Rs. 6500. The key is to find k first, then apply the combined discount.

Multiple choice

An article is sold for Rs. 372 after two successive discounts of 25% and 38% on its marked price. Total discount (in Rs.) is:

  1. 380

  2. 420

  3. 428

  4. 455
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the marked price be M. After a 25% discount, the price becomes 0.75M. After a further 38% discount, the final selling price is 0.75M × 0.62 = 0.465M. Given that the selling price is Rs. 372, we have 0.465M = 372, so M = 372/0.465 = Rs. 800. The total discount is Rs. 800 - Rs. 372 = Rs. 428. Option A (380) is the marked price minus the selling price, not accounting for successive discounts correctly. Options B and D are computational errors.

Multiple choice

Anil bought two articles A and B at a total cost of Rs. 10,000. He sold the article A at 15% profit and the article B at 10% loss. In the whole deal, he made no profit or no loss. Find the selling price of the article A.

  1. Rs. 4,200

  2. Rs. 5,200

  3. Rs. 4,800

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

Let cost price of A = x, then cost price of B = (10000 - x). Selling price of A = 1.15x (15% profit), selling price of B = 0.9(10000 - x) (10% loss). Since there's no profit or loss overall: 1.15x + 0.9(10000 - x) = 10000. Solving: 1.15x + 9000 - 0.9x = 10000, so 0.25x = 1000 and x = 4000. Therefore, selling price of A = 1.15 × 4000 = Rs. 4,600.

Multiple choice

A shopkeeper marked every item 25% above the cost price and allowed 10% discount. Shruti being a regular customer got 5% additional discount on the bill and paid Rs. 2394 for the item purchased. What is the cost price of the item (in Rs.)?

  1. 2240

  2. 2440

  3. 2140

  4. 2010
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let CP = x. Marked price = x + 0.25x = 1.25x. After 10% discount: 1.25x × 0.9 = 1.125x. After additional 5% discount: 1.125x × 0.95 = 1.06875x. Since Shruti pays Rs. 2394, we have 1.06875x = 2394, giving x = 2394/1.06875 = Rs. 2240.