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
131
A, B and C become partners in a business. A contributes 1/3rd of the capital for 1/4th of the time. B contributes 1/5th of the capital for 1/6th of the time. C contributes the rest of the capital for the whole time. If the profit is Rs. 1820, A's share is:
Answer:
Rs. 260
C's capital = 1 - (1/3 + 1/5) = 7/15. Profit ratio = (1/3 * 1/4) : (1/5 * 1/6) : (7/15 * 1) = 1/12 : 1/30 : 7/15. Multiply by 60: 5 : 2 : 28. Total parts = 35. A's share = (5/35) * 1820 = 1/7 * 1820 = Rs. 260.
132
P and Q start a business with initial investments in the ratio of 5:4. Their corresponding annual profits are in the ratio of 5:8. If P invested his money for 6 months, for how many months did Q invest his money?
Answer:
12 months
Let Q's time be t. Profit ratio = (13 * 7) / (8 * t) = 7 / 5 => 91 / 8t = 7 / 5 => 455 = 56t => t = 8.125. Let me change numbers. Let ratio be 5:4, profits 5:8. P time 6 months. (5*6)/(4*t) = 5/8 => 30/4t = 5/8 => t=12. Let's rewrite the question.
133
X, Y and Z enter into a partnership. X invests Rs. 30,000. Y invests Rs. 40,000. Z invests Rs. 50,000. After 4 months, X withdraws half his capital and Y adds Rs. 10,000. At the end of the year, what is the ratio of their profits?
Answer:
6:14:15
X = (30*4) + (15*8) = 120 + 120 = 240. Y = (40*4) + (50*8) = 160 + 400 = 560. Z = 50 * 12 = 600. Ratio = 240:560:600 = 24:56:60 = 6:14:15. Wait, 6:14:15 is not in options. Let me recompute: X = (30*4)+(15*8) = 240. Y = (40*4)+(50*8)=560. Z = (50*12)=600. Ratio = 240:560:600 = 6:14:15. Let me change the options to match.
134
A and B entered into a business. A invested Rs. 40,000 and B invested Rs. 60,000. After 6 months, A invested an additional Rs. 20,000 while B withdrew Rs. 10,000. If the total profit after one year is Rs. 31,500, what is A's share?
Answer:
Rs. 15000
A = (40k * 6) + (60k * 6) = 240k + 360k = 600k. B = (60k * 6) + (50k * 6) = 360k + 300k = 660k. Ratio = 600 : 660 = 10 : 11. Total parts = 21. A's share = 10/21 * 33000 = not integer. Let's adjust profit to 31500. A's share = 10/21 * 31500 = 15000. Let's update question profit to 31500.
135
In a partnership, A invests Rs. 20000 for 9 months and B invests Rs. 30000 for 12 months. If the total profit is Rs. 9000, what is A's share?
Answer:
Rs. 3000
Ratio = (20000*9) : (30000*12) = 180000 : 360000 = 1 : 2. Total parts = 3. A's share = 1/3 * 9000 = Rs. 3000.
136
A, B and C rented a video cassette for Rs. 350. They used it for 6, 10 and 12 hours respectively. The rent to be paid by B is:
Answer:
Rs. 125
Rent ratio = 6:10:12 = 3:5:6. Total parts = 14. B's rent = (5/14) * 350 = 5 * 25 = Rs. 125.
137
A starts a business with Rs. 50,000. 3 months later B joins with Rs. 70,000. Another 3 months later C joins with Rs. 80,000. At the end of the year, the profit is Rs. 28,500. What is the difference between A's and C's share?
Answer:
Rs. 2000
A's time = 12, B's time = 9, C's time = 6. Ratio = (50*12) : (70*9) : (80*6) = 600 : 630 : 480 = 20 : 21 : 16. Total parts = 57. 30000 / 57 is not integer. Let's make profit Rs. 28500. Difference = A(20) - C(16) = 4 parts. 1 part = 28500 / 57 = 500. Difference = 4 * 500 = Rs. 2000. I'll update question.
138
X, Y, Z start a business. X's investment is 3 times Y's investment and Y's investment is 2/3 of Z's investment. What is the ratio of their profits?
Answer:
6:2:3
Let Z = 3. Then Y = 2/3 * 3 = 2. X = 3 * 2 = 6. Ratio = X:Y:Z = 6:2:3.
139
A, B and C enter into a partnership. A invests Rs. 24000, B invests Rs. 32000, and C invests Rs. 18000. A withdraws his capital after 8 months. B withdraws after 10 months. C stays for the whole year. If total profit is Rs. 18200, find B's share.
Answer:
Rs. 8000
Ratio = (24*8) : (32*10) : (18*12) = 192 : 320 : 216 = 24 : 40 : 27. Total parts = 91. 18500 is not divisible by 91. Let's adjust total profit to Rs. 18200. B's share = (40/91)*18200 = 8000. I will update the question.
140
Two friends A and B invest Rs. 10,000 and Rs. 12,000 respectively in a business. They agree to share 25% of the profit equally and the rest according to their investments. If B gets Rs. 375 more than A, what is the total profit?
Answer:
Rs. 5500
Ratio of investments = 10000 : 12000 = 5 : 6. 75% of total profit (0.75P) is divided in this ratio. Difference = (1/11) of 0.75P = 350 => 0.75P = 3850 => P = 3850 / 0.75 = 5133.33. Let me adjust the difference to make it an integer. If difference is Rs. 210, then 0.75P = 2310 => P = 3080. If difference is Rs. 300, 0.75P = 3300 => P = 4400. If difference is Rs. 375, 0.75P = 4125 => P = 5500. Let's use 375.