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
111
A began a business with Rs. 2250 and was joined afterwards by B with Rs. 2700. If the profit at the end of the year was divided in the ratio 2:1, after how much time did B join?
Answer:
7 months
Let B's time be t. (2250 * 12) / (2700 * t) = 2/1 => 27000 / 2700t = 2 => 10 / t = 2 => t = 5 months. Since B was in the business for 5 months, he joined after 12 - 5 = 7 months.
112
P and Q start a business with Rs. 14000 and Rs. 18000. After 4 months, P withdraws his entire capital. At the end of the year, what is the ratio of their profits?
Answer:
7:27
P's time = 4 months. Q's time = 12 months. Ratio = (14000*4) : (18000*12) = 56 : 216 = 7 : 27.
113
A, B and C invest their capitals in the ratio 2:3:4 and the time period of their investments are in the ratio 4:5:6. Find the ratio of their profits.
Answer:
8:15:24
Profit ratio = (Capital A * Time A) : (Capital B * Time B) : (Capital C * Time C) = (2*4) : (3*5) : (4*6) = 8 : 15 : 24.
114
A and B entered into a business with investments of Rs. 10000 and Rs. 15000. After 6 months, A withdrew Rs. 2000 and B withdrew Rs. 3000. If the profit is Rs. 8000, what is A's share?
Answer:
Rs. 3200
A = (10000*6) + (8000*6) = 108000. B = (15000*6) + (12000*6) = 162000. Ratio = 108:162 = 2:3. Total parts = 5. A's share = (2/5) * 7800 = 2 * 1560 = Rs. 3120. Wait, 7800/5 = 1560. 2*1560=3120. Options don't match. Let me adjust profit to Rs. 8000. A's share = (2/5)*8000 = 3200.
115
Raju, Shyam and Hari entered into a partnership investing Rs. 15000, Rs. 18000 and Rs. 24000. After 6 months, Raju adds Rs. 5000. What will be the ratio of their profits at the end of the year?
Answer:
35:36:48
Raju = (15000*6) + (20000*6) = 90000 + 120000 = 210000. Shyam = 18000 * 12 = 216000. Hari = 24000 * 12 = 288000. Ratio = 210 : 216 : 288. Divide by 6 = 35 : 36 : 48.
116
A, B and C are partners. A receives 2/5 of the profit, B receives 1/3 of the profit, and C receives the remaining Rs. 1200. What is A's share?
Answer:
Rs. 1800
C's share of profit = 1 - (2/5 + 1/3) = 1 - 11/15 = 4/15. Let total profit be P. (4/15)P = 1200 => P = 4500. A's share = (2/5) * 4500 = Rs. 1800.
117
X and Y invest in a business in the ratio 3:2. If 10% of total profit goes to charity and X's share is Rs. 1350, the total profit is:
Answer:
Rs. 2500
Profit after charity = 90% of P. X's share = (3/5) * 0.90P = 0.54P. Given 0.54P = 1350 => P = 1350 / 0.54 = Rs. 2500.
118
A, B and C invest Rs. 5000, Rs. 6000 and Rs. 4000 respectively in a business. A gets 30% of the profit for managing the business. The remaining profit is distributed according to their investments. If the total profit is Rs. 5000, what is the total amount received by A?
Answer:
Rs. 2666
A's salary = 30% of 5000 = 1500. Remaining profit = 3500. Ratio = 5:6:4. Total parts = 15. A's profit share = (5/15) * 3500 = 1/3 * 3500 = 1166.67. Total = 1500 + 1166.67 = 2666.67.
119
P starts a business with Rs. 4000. After some months, Q joins with Rs. 5000. If the profit is distributed equally at the end of the year, after how many months did Q join?
Answer:
2.4 months
Let Q's time be t. (4000*12) / (5000*t) = 1/1 => 48000 = 5000t => t = 9.6 months. Q joined after 12 - 9.6 = 2.4 months.
120
A invests Rs. 3000 for 12 months. B invests Rs. 4000 for 9 months. C invests Rs. 5000 for 6 months. If they earn a total profit of Rs. 5100, what is B's share?
Answer:
Rs. 1800
Ratio = (3000*12) : (4000*9) : (5000*6) = 36 : 36 : 30 = 6 : 6 : 5. Total parts = 17. B's share = (6/17) * 5100 = 6 * 300 = Rs. 1800.