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
101
X, Y and Z enter a partnership. X contributes Rs. 3200 for 4 months, Y contributes Rs. 5100 for 3 months, and Z contributes Rs. 2700 for 5 months. The total profit is Rs. 1248. Find X's share.
Answer:
Rs. 384
Ratio = (3200*4) : (5100*3) : (2700*5) = 12800 : 15300 : 13500 = 128 : 153 : 135. Total parts = 416. X's share = (128/416) * 1248 = 128 * 3 = Rs. 384.
102
A started a business with Rs. 10,000. B joins after 2 months with Rs. 20,000. C joins after another 2 months with Rs. 30,000. If the total profit is Rs. 11,200, find C's share.
Answer:
Rs. 4800
Time: A = 12, B = 10, C = 8. Ratio = (10*12) : (20*10) : (30*8) = 120 : 200 : 240 = 6 : 10 : 12 = 3 : 5 : 6. Total parts = 14. 12000 / 14 is not integer. Let's adjust total profit to Rs. 14000. C's share = (6/14)*14000 = 6000. Or profit = 11200, C's = 4800.
103
A, B and C invest in a business. A's investment is 3 times B's, and B's investment is 2/3 of C's. If the total profit is Rs. 6600, find B's share.
Answer:
Rs. 1200
Let C = 3x. B = 2x. A = 6x. Ratio A:B:C = 6:2:3. Total parts = 11. B's share = (2/11) * 6600 = Rs. 1200.
104
P and Q start a business with Rs. 50,000 and Rs. 40,000. After 4 months, P withdraws half his capital and Q adds half his capital. R joins with Rs. 70,000. After a year, what is the profit ratio of P, Q and R?
Answer:
All of the above
P = (50*4) + (25*8) = 200 + 200 = 400. Q = (40*4) + (60*8) = 160 + 480 = 640. R = 70*8 = 560. Ratio = 400:640:560 = 40:64:56. Wait, Q is 640. So 40:64:56 => 5:8:7. Option a has 68. Let me re-read. Q adds half his capital. 40 + 20 = 60. 60*8 = 480. 160+480 = 640. Let me change option a to 40:64:56.
105
In a partnership, A invests Rs. 1/4 of total capital for 1/4 of the time. B invests 1/5 of total capital for 1/5 of the time. C invests the rest of the capital for the whole time. Find the ratio of their profits.
Answer:
25:16:220
C's capital = 1 - (1/4 + 1/5) = 11/20. Profit ratio = (1/4 * 1/4) : (1/5 * 1/5) : (11/20 * 1) = 1/16 : 1/25 : 11/20. Multiply by 400 (LCM of 16, 25, 20): 25 : 16 : (11*20) = 25 : 16 : 220. Wait, 400/20 = 20. 11*20 = 220. So 25:16:220. Let me check option a.
106
A started a business with Rs. 76000. After some months, B joined with Rs. 57000. At the end of the year, the total profit was divided in the ratio 2:1. After how many months did B join?
Answer:
4 months
Let B's time be t. (76000*12) / (57000*t) = 2/1 => 912 / 57t = 2/1 => 16 / t = 2/1 => 2t = 16 => t = 8. B joined after 12 - 8 = 4 months.
107
A, B and C invest Rs. 1000, Rs. 1500, and Rs. 2000 respectively. If B gets Rs. 600 as his share of profit, what is the total profit?
Answer:
Rs. 1800
Ratio = 1000:1500:2000 = 2:3:4. Total parts = 9. B's share is 3 parts = 600 => 1 part = 200. Total profit = 9 parts = Rs. 1800.
108
X and Y invest Rs. 21000 and Rs. 17500 in a business. At the end of the year, they make a profit of Rs. 26400. What is X's share?
Answer:
Rs. 14400
Ratio = 21000 : 17500 = 210 : 175 = 6 : 5. Total parts = 11. X's share = (6/11) * 26400 = 6 * 2400 = Rs. 14400.
109
Two partners A and B invest Rs. 40,000 and Rs. 50,000 respectively. A receives 15% of the total profit for managing the business, and the rest is divided according to their investments. If total profit is Rs. 18,000, find B's share.
Answer:
Rs. 8500
A's salary = 15% of 18000 = 2700. Remaining profit = 15300. Ratio = 40:50 = 4:5. Total parts = 9. B's share = (5/9) * 15300 = 5 * 1700 = Rs. 8500.
110
A starts a business with Rs. 3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2:3. What is B's contribution?
Answer:
Rs. 9000
Let B's capital be x. A's time = 12, B's time = 7. (3500 * 12) / (x * 7) = 2/3 => 42000 / 7x = 2/3 => 6000 / x = 2/3 => 2x = 18000 => x = 9000.