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 and C invest Rs. 6000, Rs. 8000 and Rs. 10000. A gets 20% of profit for managing. Rest is distributed by capital. Total profit is Rs. 7500. Find A's total share.
Answer:
Rs. 3000
A's salary = 20% of 7500 = 1500. Remaining profit = 6000. Ratio = 6:8:10 = 3:4:5. Total parts = 12. A's profit = (3/12) * 6000 = 1500. Total A = 1500 + 1500 = Rs. 3000.
142
A and B invest in ratio 3:4. If they share profit in ratio 1:2 and A invested for 8 months, for how many months did B invest?
Answer:
12 months
Let B's time be t. (3 * 8) / (4 * t) = 1/2 => 24 / 4t = 1/2 => 6 / t = 1/2 => t = 12 months.
143
P, Q, R invest in ratio 4:5:6. R gets Rs. 4000 more than P. Find total profit.
Answer:
Rs. 30000
R - P = 6 - 4 = 2 parts. 2 parts = 4000 => 1 part = 2000. Total profit = 15 parts = 15 * 2000 = Rs. 30000.
144
A and B invest Rs. 15000 and Rs. 20000. A withdraws Rs. 5000 after 6 months. B adds Rs. 5000 after 6 months. Profit ratio?
Answer:
5:9
A = (15*6) + (10*6) = 150. B = (20*6) + (25*6) = 270. Ratio = 150 : 270 = 15 : 27 = 5 : 9. Let me check my options. 5:9 is not there. Let's provide 5:9 in Option C.
145
X, Y and Z invest Rs. 18000, Rs. 24000 and Rs. 30000. Z gets 5% of profit for managing. Rest is distributed by capital. Total profit is Rs. 14400. Find Z's total share.
Answer:
Rs. 6420
Z's salary = 5% of 14400 = 720. Remaining profit = 13680. Ratio = 18:24:30 = 3:4:5. Total parts = 12. Z's profit = (5/12) * 13680 = 5 * 1140 = 5700. Total Z = 720 + 5700 = Rs. 6420.
146
A starts a business with Rs. 30000. B joins after 4 months with Rs. 40000. C joins after another 4 months with Rs. 50000. Find the profit ratio.
Answer:
9:8:5
A=12, B=8, C=4. Ratio = (30*12) : (40*8) : (50*4) = 360 : 320 : 200 = 36 : 32 : 20 = 9 : 8 : 5.
147
A, B and C enter into a partnership. A invests Rs. 5000 for 12 months, B invests Rs. 6000 for 8 months, and C invests Rs. 8000 for 5 months. If C gets Rs. 2000, what is the total profit?
Answer:
Rs. 7400
Ratio = (5000*12) : (6000*8) : (8000*5) = 60000 : 48000 : 40000 = 60 : 48 : 40 = 15 : 12 : 10. Total parts = 37. C's share is 10 parts = 2000 => 1 part = 200. Total profit = 37 * 200 = Rs. 7400.
148
P, Q, R invest in a business. P invests 1/5 of the total capital for 1/2 of the time. Q invests 1/3 of the total capital for 1/4 of the time. R invests the remaining capital for the whole time. Find the ratio of their profits.
Answer:
6:5:28
R's capital = 1 - (1/5 + 1/3) = 1 - 8/15 = 7/15. Profit ratio = (1/5 * 1/2) : (1/3 * 1/4) : (7/15 * 1) = 1/10 : 1/12 : 7/15. Multiply by 60: 6 : 5 : 28.
149
A and B invest Rs. 10000 and Rs. 12000. After 4 months A withdraws Rs. 2000 and B adds Rs. 3000. After another 4 months C joins with Rs. 15000. Profit ratio?
Answer:
26:42:15
A = (10*4) + (8*8) = 40 + 64 = 104. B = (12*4) + (15*8) = 48 + 120 = 168. C = 15 * 4 = 60. Ratio = 104 : 168 : 60 = 26 : 42 : 15. Wait, 168 / 4 = 42. Option A has 33. My bad: B adds 3000, so B becomes 15000. 12*4 = 48, 15*8 = 120. 48+120=168. C joins after 8 months, so C's time is 4 months. 15*4 = 60. Ratio 104:168:60 => 26:42:15. I will change option A to 26:42:15.
150
X starts a business with Rs. 15000. Y joins after 3 months with Rs. 20000. Z joins after 6 months with Rs. 30000. Find the profit ratio.
Answer:
1:1:1
X=12, Y=9, Z=6. Ratio = (15*12) : (20*9) : (30*6) = 180 : 180 : 180 = 1 : 1 : 1.