CET 2026 Profit & Loss
Q1. The marked price of an article is ₹2500. Two successive discounts of 10% and 5% are allowed. Even then, the shopkeeper earns a 20% profit. Find the cost price of the article.
Correct Option: E
Rationale: SP = 2500 × 90/100 × 95/100 = ₹2137.50.
Since SP = 120% of CP, CP = 2137.50 × 100/120 = ₹1781.25.
Q2. A shopkeeper marks an article 40% above its cost price. He offers a two-stage discount — first a 10% discount, and then an additional 5% discount. Find his overall profit percentage if the cost price is ₹200.
Correct Option: D
Rationale: MP = 200 × 140% = ₹280.
After successive discounts, SP = 280 × 90% × 95% = ₹239.40.
Profit = ₹39.40, so profit% = 39.40 / 200 × 100 = 19.7%.
Q3. A person bought a book and a novel for ₹2800. He sold the book at 10% profit and the novel at 12.5% profit. If his overall profit was 13%, then what is the difference between the cost prices of the book and the novel?
Correct Option: F (No valid option)
Rationale: This question is mathematically inconsistent because the individual profits are 10% and 12.5%. Therefore, the combined overall profit percentage must lie between 10% and 12.5%; it cannot be 13%.
Q4. The profit earned by selling an article for ₹900 is double the loss incurred when the same article is sold for ₹450. At what price should the article be sold to make a 25% profit?
Correct Option: B
Rationale: Let CP = x. Then 900 − x = 2(x − 450) ⇒ 3x = 1800 ⇒ CP = ₹600.
For 25% profit, SP = 600 × 125% = ₹750.
Q5. A fan is listed at ₹1500 and a discount of 20% is offered on the list price. What additional discount must be offered to the customer to bring the net price to ₹1104?
Correct Option: A
Rationale: After 20% discount, price = 1500 × 80% = ₹1200.
Required reduction = 1200 − 1104 = ₹96.
Additional discount = 96 / 1200 × 100 = 8%.
Q6. The marked price of an article is ₹25. A discount of 10% is given. How much should be the selling price so that the shopkeeper gains 10%?
Correct Option: F (Question incomplete/inconsistent)
Rationale: A 10% discount on ₹25 gives SP = ₹22.50, but to determine what the SP *should* be for a 10% gain, the actual cost price must also be known.
Q7. A dishonest shopkeeper uses a 900 gram weight instead of a 1 kilogram weight. He sells goods per kilogram at the same price at which he buys one kilogram. What is his profit percentage?
Correct Option: B
Rationale: He charges the cost of 1000 g but gives only 900 g.
Profit% = (100 / 900) × 100 = 11 1/9%.
Q8. A person sold an article for ₹3600 and got a profit of 20%. Had he sold the article for ₹3150, how much profit would he have got?
Correct Option: B
Rationale: CP = 3600 / 1.20 = ₹3000.
At ₹3150, profit = ₹150.
So profit% = (150 / 3000) × 100 = 5%.
Q9. A sells an article to B at a profit of 20%. B sells it to C at a profit of 25%. C sells it to D at a loss of 10%. D sells it back to A at a profit of 12 1/2%. If A finally pays ₹486 to get back the article, what was the original cost price of the article for A?
Correct Option: B
Rationale: If original CP = x, final price = x × 1.20 × 1.25 × 0.90 × 1.125 = 1.51875x.
Thus 1.51875x = 486 ⇒ x = ₹320.
Q10. A trader first incurs a loss of x% on an article and then makes a profit of y%. If the final selling price equals the original cost price, then the relation between x and y is:
Correct Option: B
Rationale: After x% loss, value = (100 − x)%. To recover to 100 after y% profit:
(100 − x)(100 + y) = 10000 ⇒ y = 100x / (100 − x).
Q11. A trader sells his articles at 10% higher than their original price. Due to higher demand, he again increases the price by 15%. Calculate the percentage of profit the trader makes.
Correct Option: B
Rationale: Successive increases of 10% and 15% give 1.10 × 1.15 = 1.265.
So the overall profit is 26.5%.
Q12. A person sold a radio at a loss of 5%. Had he sold it for ₹210 more, he would have gained 25%. For what value should he sell it in order to gain 35%?
Correct Option: B
Rationale: Difference between 25% profit and 5% loss = 30% of CP = ₹210.
Thus CP = ₹700.
For 35% profit, SP = 700 × 1.35 = ₹945.
Q13. Mahan bought a bag with a 15% discount on the labeled price. He sold the bag for ₹2880 with a 20% profit on the labeled price. At what price did he buy the bag?
Correct Option: C
Rationale: SP ₹2880 represents 120% of labeled price, so labeled price = ₹2400.
Buying at 15% discount gives CP = 2400 × 85% = ₹2040.
Q14. By selling 12 oranges for a rupee, a man loses 20%. How many oranges for a rupee should he sell to gain 20%?
Correct Option: A
Rationale: At 20% loss, CP of 12 oranges = ₹1 / 0.8 = ₹1.25.
For 20% gain, required SP = ₹1.50 for 12 oranges.
Hence for ₹1, number of oranges = 12 / 1.5 = 8.
Q15. A man bought an article and sold it at a gain of 5%. If he had bought it at 5% less and sold it for ₹1 less, he would have made a profit of 10%. The cost price of the article is:
Correct Option: C
Rationale: Let original CP = x. Original SP = 1.05x.
New CP = 0.95x and new SP = 1.05x − 1.
Since this gives 10% profit, 1.05x − 1 = 1.10 × 0.95x = 1.045x
⇒ 0.005x = 1 ⇒ x = ₹200.
