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
191
X and Y are partners. X invests Rs. 5000 for 12 months. Y invests Rs. 6000 for 5 months. If the profit of X is Rs. 1200, find the total profit.
Answer:
Rs. 1800
Ratio = (5000*12) : (6000*5) = 60 : 30 = 2 : 1. X's share is 2 parts = 1200 => 1 part = 600. Total profit = 3 parts = Rs. 1800.
192
A, B and C invest Rs. 5000, Rs. 6000 and Rs. 4000. A is an active partner and gets 15% of the total profit. If total profit is Rs. 4500, what is A's total share?
Answer:
Rs. 1950
A's salary = 15% of 4000 = 600. Remaining profit = 3400. Ratio = 5:6:4. Total parts = 15. A's profit = (5/15) * 3400 = 1/3 * 3400 = 1133.33. Total A = 600 + 1133.33 = Rs. 1733.33. My options don't match. Let's make total profit 4500. A's salary = 675. Rem = 3825. A's profit = 1/3 * 3825 = 1275. Total = 1950. Let's use 4500.
193
A starts a business with Rs. 21000. B joins later with Rs. 36000. If the profit is divided equally at the end of the year, for how many months did B invest his money?
Answer:
7 months
Let B's time be t. (21000 * 12) / (36000 * t) = 1/1 => 252000 = 36000t => t = 7 months.
194
X, Y and Z enter into a partnership. X invests Rs. 8000 for 12 months, Y invests Rs. 10000 for 9 months and Z invests Rs. 12000 for 6 months. If the total profit is Rs. 8600, find Y's share.
Answer:
Rs. 3000
Ratio = (8000*12) : (10000*9) : (12000*6) = 96 : 90 : 72 = 32 : 30 : 24 = 16 : 15 : 12. Total parts = 43. Y's share = (15/43) * 8600 = 15 * 200 = Rs. 3000.
195
In a partnership, A invests Rs. 10000 for 3 months, B invests Rs. 12000 for 4 months and C invests Rs. 15000 for 2 months. Find the ratio of their profits.
Answer:
5:8:5
Ratio = (10000*3) : (12000*4) : (15000*2) = 30000 : 48000 : 30000 = 30 : 48 : 30 = 5 : 8 : 5.
196
A, B, C start a business. A invests Rs. 20,000, B invests Rs. 30,000, C invests Rs. 40,000. B gets 10% of profit for managing, C gets 15% for managing. Remaining is distributed by capital. Total profit is Rs. 18,000. What is A's share?
Answer:
Rs. 3000
Total salary = 25% of 18000 = 4500. Remaining = 13500. Ratio = 2:3:4. Total parts = 9. A's share = (2/9) * 13500 = 2 * 1500 = Rs. 3000.
197
P, Q, R are partners. P's capital is 1/4 of total, Q's is 1/3 of total, and R's is the rest. Profit is distributed equally because P and Q are active. Wait, let's make a standard question. P invests 1/4, Q 1/3, R the rest. Total profit is 6000. R's share?
Answer:
Rs. 2500
R's capital = 1 - (1/4 + 1/3) = 1 - 7/12 = 5/12. Profit is distributed in ratio of capitals. R's share = 5/12 * 6000 = 5 * 500 = Rs. 2500.
198
A, B and C invest their capitals in the ratio 3:4:5. After 6 months, A adds 50% of his capital, B adds 25% of his capital, and C withdraws 20% of his capital. Find the profit ratio at the end of the year.
Answer:
15:18:18
A = (3*6) + (4.5*6) = 18 + 27 = 45. B = (4*6) + (5*6) = 24 + 30 = 54. C = (5*6) + (4*6) = 30 + 24 = 54. Ratio = 45 : 54 : 54 = 15 : 18 : 18. Wait, C withdraws 20%, so 5 - 1 = 4. 30 + 24 = 54. Ratio is 15:18:18. Let me check option a.
199
Four milkmen A, B, C, D rent a pasture. A grazed 12 cows for 4 months, B 15 cows for 3 months, C 18 cows for 6 months, and D 24 cows for 2 months. If total rent is Rs. 1245, find A's share.
Answer:
Rs. 240
Ratio = (12*4) : (15*3) : (18*6) : (24*2) = 48 : 45 : 108 : 48. Total parts = 249. A's share = (48/249) * 1245 = 48 * 5 = Rs. 240.
200
A and B entered into a business investing Rs. 50000 and Rs. 60000. A is an active partner and gets 10% of profit as salary. If B gets Rs. 27000 as his share of profit, what is the total profit?
Answer:
Rs. 55000
Ratio of investment = 5:6. B gets 6/11 of the remaining profit (which is 90% of total). B's share = (6/11) * 0.9P = 27000. 0.9P = (27000 * 11) / 6 = 4500 * 11 = 49500. P = 49500 / 0.9 = Rs. 55000.