Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
231
An article is marked at Rs. 10,000. A shopkeeper offers 3 successive discounts of 10%, 20% and 30%. What is the final selling price?
Answer:
Rs. 5040
Final SP = Marked Price * (1 - d1) * (1 - d2) * (1 - d3). SP = 10000 * 0.90 * 0.80 * 0.70 = 10000 * 0.504 = Rs. 5040.
232
If the cost price is 25% of selling price, then what is the profit percent?
Answer:
300%
Let Selling Price (SP) = 100. Then Cost Price (CP) = 25. Profit = SP - CP = 100 - 25 = 75. Profit % = (Profit / CP) * 100 = (75 / 25) * 100 = 300%.
233
A sold an article to B at 10% profit. B sold it to C at 20% profit. C sold it to D at 25% profit. If D paid Rs. 3300, what did A pay for it?
Answer:
Rs. 2000
Let A's CP be x. B's CP = 1.1x. C's CP = 1.1x * 1.2 = 1.32x. D's CP = 1.32x * 1.25 = 1.65x. We are given 1.65x = 3300. x = 3300 / 1.65 = 2000. A paid Rs. 2000.
234
A publisher prints 2000 copies of a book at a cost of Rs. 70,000. He distributes 400 copies free as specimens. He gives a 30% discount on the marked price and still makes a 20% profit. What is the marked price of each book?
Answer:
Rs. 75
Total cost = 70,000. Desired profit = 20%, so Total SP = 70,000 * 1.20 = 84,000. Only 1600 copies are sold (2000 - 400 free). SP per book = 84,000 / 1600 = Rs. 52.5. This SP is after a 30% discount on MP. So, 70% of MP = 52.5 => MP = 52.5 / 0.7 = 75. The marked price is Rs. 75.
235
A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
Answer:
30%
Let CP = 100. Profit = 23.5%, so SP = 123.5. This SP is after a 5% discount on MP. So, 95% of MP = 123.5 => MP = 123.5 / 0.95 = 130. If no discount is offered, SP = MP = 130. Profit = 130 - 100 = 30. Profit % = 30%.
236
If goods be purchased for Rs. 450, and one-third is sold at a loss of 10%. At what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
Answer:
35%
Total CP = 450. Desired total profit = 20% of 450 = Rs. 90. CP of one-third = 450 / 3 = 150. Loss on this part = 10% of 150 = Rs. 15. The remaining part has CP = 300. Let the profit on this be P. Total profit = P - 15 = 90 => P = 105. Profit % on remaining = (105 / 300) * 100 = 35%.
237
A shopkeeper allows a 10% discount on the marked price of an item and still gains 17%. If the marked price is Rs. 260, find the cost price of the item.
Answer:
Rs. 200
MP = 260. Discount = 10% of 260 = 26. SP = 260 - 26 = 234. Gain is 17%, so SP = 117% of CP. 1.17 * CP = 234 => CP = 234 / 1.17 = 200. Cost price = Rs. 200.
238
A person bought a machine and sold it at a 10% profit. If he had bought it for 20% less and sold it for Rs. 10 more, he would have gained 40%. The cost price of the machine was:
Answer:
Rs. 500
Let CP = x. Original SP = 1.10x. New CP = x - 20% = 0.80x. New SP = 1.10x + 10. Gain on new CP = 40%, so New SP = 1.40 * (0.80x) = 1.12x. Equating the two SPs: 1.10x + 10 = 1.12x => 0.02x = 10 => x = 10 / 0.02 = 500. Cost price = Rs. 500.
239
The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make a 25% profit?
Answer:
Rs. 2000
Since the profit and loss percentages are equal, the CP is the exact average of the two selling prices. CP = (1920 + 1280) / 2 = 3200 / 2 = 1600. To make a 25% profit, SP = 1600 * 1.25 = Rs. 2000.
240
A manufacturer offers a 20% discount on marked price but still makes a 20% profit. If the cost of manufacturing increases by 10%, what discount should he offer on the same marked price to maintain the same profit margin of 20%?
Answer:
12%
Let CP = 100. Profit = 20%, so SP = 120. With 20% discount, MP = 120 / 0.8 = 150. New CP = 100 + 10% = 110. To maintain 20% profit, new SP = 110 * 1.2 = 132. New discount = MP - new SP = 150 - 132 = 18. Discount % = (18 / 150) * 100 = 12%.