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
121
A and B entered into a partnership investing Rs. 10000 and Rs. 15000. After 3 months, A adds Rs. 5000 and B adds Rs. 5000. What is the ratio of their profits at the end of the year?
Answer:
11:15
A = (10000*3) + (15000*9) = 30000 + 135000 = 165000. B = (15000*3) + (20000*9) = 45000 + 180000 = 225000. Ratio = 165 : 225 = 33 : 45 = 11 : 15. Let me re-divide: 165 / 15 = 11. 225 / 15 = 15. So 11:15. I'll pick A.
122
P, Q and R start a business. P invests 3 times as much as Q invests and Q invests 2/3rd of what R invests. Find the ratio of capitals of P, Q and R.
Answer:
6:2:3
Let R = 3x. Then Q = 2x. P = 3 * 2x = 6x. Ratio P:Q:R = 6x : 2x : 3x = 6:2:3.
123
A, B and C invest in a business. The investment of A is twice the investment of B and the investment of B is thrice the investment of C. If the total profit is Rs. 10000, find the share of B.
Answer:
Rs. 3000
Let C = x. Then B = 3x and A = 6x. Ratio A:B:C = 6:3:1. Total parts = 10. B's share = (3/10) * 10000 = Rs. 3000.
124
In a partnership, A invests Rs. 50,000 for 6 months, B invests Rs. 60,000 for 4 months, and C invests Rs. 80,000 for 5 months. If the total profit is Rs. 47,000, what is A's share?
Answer:
Rs. 15,000
Ratio = (50*6) : (60*4) : (80*5) = 300 : 240 : 400 = 30 : 24 : 40 = 15 : 12 : 20. Total parts = 47. A's share = (15/47) * 47000 = Rs. 15,000.
125
Two partners invested Rs. 50,000 and Rs. 70,000 in a business. They agreed that 70% of the profits will be divided equally and the remaining 30% will be divided according to their capitals. If one gets Rs. 900 more than the other, find the total profit.
Answer:
Rs. 18,000
Ratio = 5:7. Difference in parts = 2. Sum of parts = 12. So (2/12) of 30% of Total Profit (0.3P) = 900. (1/6) * 0.3P = 900 => 0.05P = 900 => P = 900 / 0.05 = 18000.
126
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. What is the difference between the profit shares of A and C?
Answer:
Rs. 600
Ratio = 8:10:12 = 4:5:6. B's share is 5 parts = 1500 => 1 part = 300. Difference between A and C = 6 - 4 = 2 parts. 2 * 300 = Rs. 600.
127
A, B and C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
Answer:
Rs. 14,700
Let C = x. B = x + 5000. A = x + 9000. A+B+C = 3x + 14000 = 50000 => 3x = 36000 => x = 12000. C = 12000, B = 17000, A = 21000. Ratio A:B:C = 21:17:12. Total parts = 50. A's share = (21/50) * 35000 = 21 * 700 = Rs. 14,700.
128
Raju and Sanju invest Rs. 3000 and Rs. 4000 in a business. Raju is the manager and takes Rs. 100 per month out of the profit. The rest of the profit is divided according to their capitals. If the total profit in a year is Rs. 2600, what is Raju's total share?
Answer:
Rs. 1800
Raju's salary for year = 100 * 12 = 1200. Remaining profit = 2600 - 1200 = 1400. Ratio = 3000:4000 = 3:4. Total parts = 7. Raju's profit share = (3/7)*1400 = 600. Total Raju gets = 1200 + 600 = Rs. 1800.
129
A started a business with Rs. 50000. After 4 months B joined with Rs. 60000 and after another 2 months C joined with Rs. 70000. At the end of the year, what is B's share if the total profit is Rs. 37500?
Answer:
Rs. 12000
A's time=12, B's time=8, C's time=6. Ratio = (50*12) : (60*8) : (70*6) = 600 : 480 : 420 = 60:48:42 = 10:8:7. Total parts = 25. Profit = 36000. Wait, 36000/25 = 1440. B's share = 8 * 1440 = 11520. Let's make profit 37500. 37500/25 = 1500. B = 8*1500 = 12000. I'll update profit to 37500.
130
A and B entered into a partnership investing Rs. 12000 and Rs. 15000 respectively. After 8 months, A withdraws his capital. At the end of the year, what is the ratio of their profits?
Answer:
8:15
A invested for 8 months. B invested for 12 months. Ratio = (12000*8) : (15000*12) = 96000 : 180000 = 96 : 180 = 8 : 15.