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
141
A, B, C enter a partnership with investments in ratio 5:6:8. At the end of the year they share profit in the ratio 5:3:12. Find the ratio of the time periods of their investments.
Answer:
2:1:3
Time = Profit / Investment. Ratio of times = 5/5 : 3/6 : 12/8 = 1 : 1/2 : 3/2. Multiply by 2 => 2 : 1 : 3.
142
A, B and C invest in a business. A invests Rs. 20000 for 6 months, B Rs. 15000 for 8 months, and C Rs. 10000 for 12 months. If the profit is Rs. 18000, what is the difference between B and C's share?
Answer:
Rs. 0
Ratio = (20000*6) : (15000*8) : (10000*12) = 120000 : 120000 : 120000 = 1 : 1 : 1. Since B and C have the same ratio (1:1), their shares are equal, meaning the difference is Rs. 0.
143
M starts a business with Rs. 12000. After 3 months N joins with Rs. 16000. After another 3 months, P joins with Rs. 15000. At the end of the year, if M's share is Rs. 3600, what is the total profit?
Answer:
Rs. 9450
M's time = 12, N's time = 9, P's time = 6. Ratio = (12000*12) : (16000*9) : (15000*6) = 144 : 144 : 90 = 24 : 24 : 15 = 8 : 8 : 5. M's share is 8 parts = 3600 => 1 part = 450. Total profit = 21 parts = 21 * 450 = Rs. 9450. Wait, 8:8:5 sum is 21. 21 * 450 = 9450. Let me check the options. I'll change option b to 9450.
144
A and B entered into a partnership. A contributed Rs. 5000 for 9 months and B contributed Rs. 6000 for some time. If B's profit is Rs. 1600 out of a total profit of Rs. 3100, for how long did B invest his money?
Answer:
8 months
Total profit = 3100. B's profit = 1600. A's profit = 3100 - 1600 = 1500. Profit ratio A:B = 15:16. Let B's time be t. (5000*9) / (6000*t) = 15 / 16 => 45 / 6t = 15 / 16 => 7.5 / t = 15 / 16 => 15t = 120 => t = 8 months.
145
X, Y and Z invest in a business. X invests Rs. 5000 for whole year, Y invests Rs. 4000 initially and adds Rs. 2000 after 6 months. Z invests Rs. 8000 initially and withdraws Rs. 4000 after 6 months. What is the ratio of their profits?
Answer:
5:5:6
X = 5000 * 12 = 60000. Y = (4000*6) + (6000*6) = 24000 + 36000 = 60000. Z = (8000*6) + (4000*6) = 48000 + 24000 = 72000. Ratio = 60 : 60 : 72 = 5 : 5 : 6.
146
A, B and C started a business with investments of Rs. 1500, Rs. 2500 and Rs. 3000 respectively. A receives 10% of the profit as salary. B and C receive 5% each. The rest is divided in ratio of capital. Total profit is Rs. 7000. Find C's total share.
Answer:
Rs. 2750
Total salary given = 10% + 5% + 5% = 20% of 4000 = 800. Remaining profit = 3200. Ratio = 15:25:30 = 3:5:6. Total parts = 14. 3200 / 14 is not integer. Let's make profit 3500. 20% = 700. Rem = 2800. C's profit share = (6/14)*2800 = 1200. C's total = 1200 + 175 = 1375. Let's change total profit to 7000. 20% = 1400. Rem = 5600. C's profit = (6/14)*5600 = 2400. C's salary = 5% of 7000 = 350. Total C = 2750. Let's create an exact matching question.
147
P and Q invest in a business. P invests Rs. 4000 for 8 months and Q invests Rs. 6000 for 4 months. If the profit is Rs. 2800, what is the difference between their shares?
Answer:
Rs. 400
Ratio = (4000*8) : (6000*4) = 32 : 24 = 4 : 3. Total parts = 7. Difference = 1 part. 1 part = 2800 / 7 = Rs. 400. Wait, option D is 500. Let me check: 1 part = 400. Option c is 400. Let me mark C.
148
A is a working partner and B is a sleeping partner. A invests Rs. 5000 and B invests Rs. 6000. A gets 12.5% of the profit for managing the business. If total profit is Rs. 880, what is A's total share?
Answer:
Rs. 460
A's salary = 12.5% of 880 = 1/8 * 880 = 110. Remaining profit = 880 - 110 = 770. Ratio of investment = 5:6. Total parts = 11. A's profit share = (5/11) * 770 = 350. Total A = 110 + 350 = Rs. 460.
149
A and B started a business with Rs. 15000 and Rs. 20000. After 4 months, C joins with Rs. 22500. After 9 months from the start, B withdraws his capital. If the total profit at the end of the year is Rs. 18000, find B's share.
Answer:
Rs. 6000
A's time = 12, B's time = 9, C's time = 8. Ratio = (15000*12) : (20000*9) : (22500*8) = 180000 : 180000 : 180000 = 1:1:1. B's share = 18000 / 3 = Rs. 6000.
150
A and B invest in a business in the ratio 4:5. After 10 months, B leaves the business. If the profit is distributed in the ratio 6:5, for how many months did A keep his money in the business?
Answer:
15 months
Let A's time be t. (4 * t) / (5 * 10) = 6 / 5 => 4t / 50 = 6 / 5 => 20t = 300 => t = 15 months.