All Categories MCQs
Topic Notes: All Categories
General Description
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
601
A, B, and C can complete a task in 10, 15, and 18 days respectively. They get $150 for the job. What is A's share?
Answer:
$67.5
Step 1: The ratio of their efficiencies is (1/10) : (1/15) : (1/18). Multiplying by LCM 90 gives 9:6:5. Step 2: Total parts = 9 + 6 + 5 = 20. Step 3: A's share = (9/20) * $150 = $67.5.
602
A, B, and C can do a work in 6, 8, and 12 days respectively. Together they earn $135. What is B's share?
Answer:
$45
Step 1: Efficiency ratio A:B:C = (1/6) : (1/8) : (1/12) = 4:3:2. Step 2: Total parts = 4 + 3 + 2 = 9. B's share is 3 parts. Step 3: B's share = (3/9) * $135 = $45.
603
X and Y can do a job in 20 and 30 days respectively. They complete it together and earn $100. How much does X receive?
Answer:
$60
Step 1: The ratio of efficiencies of X:Y is (1/20) : (1/30) = 3:2. Step 2: Total parts = 5. X's share corresponds to 3 parts. Step 3: X's share = (3/5) * $100 = $60.
604
A and B can complete a work in 12 and 24 days respectively. They undertake a job for $60. Find B's share.
Answer:
$20
Step 1: Efficiency ratio of A:B = (1/12) : (1/24) = 2:1. Step 2: Total parts = 3. B's share is 1 part. Step 3: B's share = (1/3) * $60 = $20.
605
A and B can do a piece of work in 10 and 15 days respectively. They work together and earn $50. What is A's share?
Answer:
$30
Step 1: Wages are divided in the ratio of efficiencies. A's eff : B's eff = (1/10) : (1/15) = 3:2. Step 2: Total parts = 5. A's share is 3 parts. Step 3: A's share = (3/5) * $50 = $30.
606
A garrison of 120 men has provisions for 200 days. After 5 days, 30 men die due to an epidemic. How long will the remaining food last?
Answer:
260 days
Step 1: After 5 days, the remaining food is enough for 120 men for 195 days. This equals 120 * 195 = 23400 man-days of food. Step 2: The remaining number of men is 120 - 30 = 90 men. Step 3: Time the food lasts = 23400 / 90 = 260 days.
607
30 men can do a work in 16 days. After 6 days, 10 men leave. In how many days will the remaining work be finished?
Answer:
15 days
Step 1: Total work = 30 * 16 = 480 man-days. Work done in 6 days = 30 * 6 = 180 man-days. Step 2: Remaining work = 480 - 180 = 300 man-days. Step 3: Remaining men = 30 - 10 = 20. Time to finish = 300 / 20 = 15 days.
608
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.
609
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.
610
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.