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
71
A contractor employs 200 men for a project of 50 days. After 40 days, he employs 50 more men and finishes on time. If he hadn't employed extra men, how many days behind schedule would he have been?
Answer:
2.5 days
Step 1: Remaining work was done by 250 men in 10 days, equal to 2500 man-days. Step 2: If no extra men were hired, 200 men would have to do the 2500 man-days of work, taking 2500 / 200 = 12.5 days. Step 3: The scheduled time left was 10 days. The delay would be 12.5 - 10 = 2.5 days.
72
50 men can do a piece of work in 40 days. After 20 days, 10 more men joined them. How many days will it now take to finish the remaining work?
Answer:
16.67 days
Step 1: Total work is 50 * 40 = 2000 man-days. Work done in 20 days = 50 * 20 = 1000 man-days. Step 2: Remaining work = 1000 man-days. Step 3: New workforce = 50 + 10 = 60 men. Time taken = 1000 / 60 = 16.67 days.
73
10 men working 6 hours a day take 18 days to finish a job. How many hours a day should 15 men work to finish it in 12 days?
Answer:
6 hours
Step 1: M1 * H1 * D1 = M2 * H2 * D2. Step 2: 10 * 6 * 18 = 15 * H2 * 12. Step 3: 1080 = 180 * H2. H2 = 1080 / 180 = 6 hours.
74
15 men working 8 hours a day can complete a task in 20 days. How many hours a day must 20 men work to complete the same task in 12 days?
Answer:
10 hours
Step 1: M1 * H1 * D1 = M2 * H2 * D2. Step 2: 15 * 8 * 20 = 20 * H2 * 12. Step 3: 2400 = 240 * H2. H2 = 2400 / 240 = 10 hours.
75
If 24 men working 8 hours a day can finish a work in 15 days, in how many days can 20 men working 9 hours a day finish it?
Answer:
16 days
Step 1: Use the formula M1 * H1 * D1 = M2 * H2 * D2. Step 2: Substitute the values: 24 * 8 * 15 = 20 * 9 * D2. Step 3: Solve for D2: 2880 = 180 * D2. D2 = 2880 / 180 = 16 days.
76
12 men can do a piece of work in 20 days. How many days will it take for 15 men to do the same work?
Answer:
16 days
Step 1: M1 * D1 = M2 * D2. Step 2: 12 * 20 = 15 * D2. Step 3: D2 = 240 / 15 = 16 days.
77
If 40 men can build a wall in 15 days, how many men are required to build the same wall in 10 days?
Answer:
60
Step 1: Use the relationship M1 * D1 = M2 * D2. Step 2: Substitute the values: 40 * 15 = M2 * 10. Step 3: Solve for M2: M2 = (40 * 15) / 10 = 600 / 10 = 60 men.
78
36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
Answer:
24 days
Step 1: Use the formula M1 * D1 = M2 * D2. Step 2: Substitute the known values: 36 * 18 = 27 * D2. Step 3: Solve for D2: D2 = (36 * 18) / 27 = 648 / 27 = 24 days.
79
6 men and 8 boys can do a piece of work in 10 days, while 26 men and 48 boys can do it in 2 days. How long will 15 men and 20 boys take to do it?
Answer:
4 days
Step 1: 10(6M + 8B) = 2(26M + 48B). 60M + 80B = 52M + 96B, giving 8M = 16B or 1M = 2B. Step 2: First group in boys: 6(2B) + 8B = 20B. 20B take 10 days, so total work is 200 B-days. Step 3: Target group: 15M + 20B = 15(2B) + 20B = 50B. Time = 200 / 50 = 4 days.
80
4 men and 6 women finish a job in 8 days. 3 men and 7 women finish it in 10 days. How many days will 10 women take?
Answer:
40 days
Step 1: 8(4M + 6W) = 10(3M + 7W). 32M + 48W = 30M + 70W, giving 2M = 22W or 1M = 11W. Step 2: Total work in terms of women: 4(11W) + 6W = 50W. 50W finish in 8 days. Step 3: So 1W takes 400 days. 10 women will take 400 / 10 = 40 days.