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
151
A, B, and C can do a piece of work in 15, 10, and 12 days respectively. They complete the work together and earn Rs 6000. What is C's share?
Answer:
Rs 2000
Efficiency ratio = (1/15) : (1/10) : (1/12) = 4 : 6 : 5. Total parts = 15. C's share = (5/15) * 6000 = Rs 2000.
152
A can do a job in 12 days and B in 20 days. They work together and earn Rs 8000. What is B's share of the earning?
Answer:
Rs 3000
Efficiency ratio of A and B = (1/12) : (1/20) = 5 : 3. Total parts = 8. B's share = (3/8) * 8000 = Rs 3000.
153
A can do a work in 10 days and B in 15 days. They undertake to do it for Rs 5000. If they work together, what is A's share?
Answer:
Rs 3000
Ratio of their efficiencies = (1/10) : (1/15) = 3 : 2. Wages are distributed based on efficiency. A's share = (3/5) * 5000 = Rs 3000.
154
A can build a wall in 30 days and B in 40 days. They work on alternate days, starting with A. The wall will be completed in:
Answer:
34.25 days
Cycle (2 days) = 1/30 + 1/40 = 7/120. 17 cycles (34 days) = 119/120. Remaining = 1/120. Next is A's turn. Time = (1/120) / (1/30) = 1/4 day. Total = 34.25 days.
155
A can do a work in 8 days and B in 12 days. They work on alternate days, starting with A. In how many days will the work be completed?
Answer:
9.5 days
Cycle (2 days) = 1/8 + 1/12 = 5/24. 4 cycles (8 days) = 20/24. Remaining = 4/24 = 1/6. Day 9 is A's turn: does 1/8. Remaining = 1/6 - 1/8 = 1/24. Day 10 is B's turn: (1/24) / (1/12) = 1/2 day. Total = 8 + 1 + 0.5 = 9.5 days.
156
A, B, and C can do a work in 12, 15, and 20 days respectively. If they work on alternate days starting with A, then B, then C, how long will it take?
Answer:
15 days
Cycle (3 days) = 1/12 + 1/15 + 1/20 = (5+4+3)/60 = 12/60 = 1/5. To complete the work, it requires 5 cycles. Total days = 5 * 3 = 15 days.
157
X can do a job in 20 days and Y in 30 days. They work on alternate days, starting with Y. When will the job be completed?
Answer:
24 days
Cycle (2 days) = 1/30 + 1/20 = 5/60 = 1/12. 12 cycles complete the work. Total days = 12 * 2 = 24 days.
158
A can finish a work in 16 days and B in 20 days. They work on alternate days, starting with A. How many days will it take to finish the work?
Answer:
17.75 days
Cycle (2 days) = 1/16 + 1/20 = 9/80. 8 cycles (16 days) = 72/80. Remaining = 8/80 = 1/10. Day 17 is A's turn: does 1/16. Remaining = 1/10 - 1/16 = 3/80. Day 18 is B's turn: (3/80) / (1/20) = 3/4 day. Total = 16 + 1 + 0.75 = 17.75 days.
159
A can do a piece of work in 10 days, and B in 15 days. They work on alternate days, starting with A. In how many days will the work be completed?
Answer:
12 days
In 2 days (1 cycle), work done = 1/10 + 1/15 = 1/6. To complete the work (1), it takes 6 cycles. Total days = 6 * 2 = 12 days.
160
2 men and 3 women can do a work in 10 days, while 3 men and 2 women can do it in 8 days. In how many days can 2 men and 1 woman do it?
Answer:
12.5 days
10(2M+3W) = 8(3M+2W) => 20M+30W = 24M+16W => 14W = 4M => 2M = 7W. Work = 10(7W+3W) = 100W-days. Group = 2M+1W = 7W+1W = 8W. Time = 100W / 8W = 12.5 days.