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
51
A can finish a work in 18 days, and B can do the same in 24 days. If they work together for 6 days, what fraction of work is left?
Answer:
5/12
Combined rate = 1/18 + 1/24 = 7/72. In 6 days, they do 6 * 7/72 = 7/12. Remaining = 1 - 7/12 = 5/12.
52
45 men can complete a work in 16 days. 6 days after they started, 30 more men joined. How many days will they take to complete the remaining work?
Answer:
6 days
45 men have 10 days of work left (450 man-days). Now there are 45 + 30 = 75 men. Time = 450 / 75 = 6 days.
53
A certain number of men can do a work in 60 days. If there were 8 men more, it could be finished in 10 days less. How many men were there initially?
Answer:
40
M * 60 = (M + 8) * 50. 60M = 50M + 400 => 10M = 400 => M = 40.
54
A and B can do a job in 12 days, B and C in 15 days, A and C in 20 days. How many days will A alone take?
Answer:
30 days
2(A+B+C) = 1/12 + 1/15 + 1/20 = 12/60 = 1/5 => A+B+C = 1/10. A = (A+B+C) - (B+C) = 1/10 - 1/15 = 1/30. A alone takes 30 days.
55
A is 40% more efficient than B. They together complete a work in 15 days. A alone can do it in:
Answer:
25.7 days
A = 1.4B. A+B = 2.4B. Work = 2.4B * 15 = 36B. A takes 36B / 1.4B = 360/14 = 180/7 = 25.71 days.
56
A can build a wall in 15 days and B in 20 days. If they work together, they earn Rs 7000. What is A's share?
Answer:
Rs 4000
Efficiency ratio = 1/15 : 1/20 = 4 : 3. Total parts = 7. A's share = (4/7) * 7000 = Rs 4000.
57
If 5 men or 9 women can finish a piece of work in 19 days, 3 men and 6 women will do the same work in:
Answer:
15 days
5M = 9W => 1M = 1.8W. 3M + 6W = 3(1.8W) + 6W = 5.4W + 6W = 11.4W. 9W take 19 days. 11.4W take (9 * 19) / 11.4 = 171 / 11.4 = 15 days.
58
A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for:
Answer:
12 days
Let total money be 84 units (LCM of 21 and 28). A's daily wage = 4. B's daily wage = 3. Together they earn 7 units per day. Time = 84 / 7 = 12 days.
59
A can do a work in 10 days, B in 15 days, and C in 20 days. A and C worked together for 2 days, and then A was replaced by B. In how many days will the total work be finished?
Answer:
8 days
A+C rate = 1/10 + 1/20 = 3/20. In 2 days = 6/20 = 3/10. Remaining = 7/10. B+C rate = 1/15 + 1/20 = 7/60. Time for B+C = (7/10) / (7/60) = 6 days. Total time = 2 + 6 = 8 days. Wait, option c is 8 days. My calculation matched 8 days, but option b is marked. Let me set the correct option.
60
20 women can do a work in 16 days. 16 men can complete the same work in 15 days. What is the ratio of the capacity of a man to a woman?
Answer:
4:3
20W * 16 = 320W-days. 16M * 15 = 240M-days. 320W = 240M => 4W = 3M => M:W = 4:3.