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
591
X can complete 1/4 of a job in 3 days, and Y can complete 1/6 of it in 4 days. How long will it take them to complete the job together?
Answer:
8 days
Step 1: X's total time = 3 * 4 = 12 days. Y's total time = 4 * 6 = 24 days. Step 2: Total work = LCM(12, 24) = 24. X's eff = 2, Y's eff = 1. Step 3: Combined eff = 3. Time taken = 24 / 3 = 8 days.
592
A can do 1/2 of a work in 5 days, and B can do 1/3 of the work in 4 days. How many days will they take working together?
Answer:
5.45 days
Step 1: A's time for full work = 5 * 2 = 10 days. B's time for full work = 4 * 3 = 12 days. Step 2: Total work = LCM(10, 12) = 60. A's eff = 6, B's eff = 5. Step 3: Combined efficiency = 11. Time = 60 / 11 = 5.45 days.
593
A and B can finish a task in 8 days, B and C in 12 days, C and A in 24 days. How many days will A alone take?
Answer:
24 days
Step 1: LCM(8, 12, 24) = 24. A+B=3, B+C=2, C+A=1. Step 2: 2(A+B+C) = 6, so A+B+C = 3. Step 3: A's efficiency = (A+B+C) - (B+C) = 3 - 2 = 1. A alone takes 24 / 1 = 24 days.
594
A and B can do a job in 10 days, B and C in 15 days, and C and A in 18 days. Working together, in how many days will they finish?
Answer:
9 days
Step 1: LCM(10, 15, 18) = 90. A+B=9, B+C=6, C+A=5. Step 2: 2(A+B+C) = 9+6+5 = 20. Therefore, A+B+C = 10. Step 3: Time taken together = 90 / 10 = 9 days.
595
A and B can do a work in 12 days, B and C in 15 days, and C and A in 20 days. How long will A, B, and C take to finish it together?
Answer:
10 days
Step 1: Total work = LCM(12, 15, 20) = 60. Efficiencies: A+B=5, B+C=4, C+A=3. Step 2: Sum of efficiencies: 2(A+B+C) = 5+4+3 = 12, so A+B+C = 6. Step 3: Time taken by all three together = 60 / 6 = 10 days.
596
A can do a work in 15 days and B in 20 days. With the help of C, they complete the work in 6 days and receive $400. What is C's share?
Answer:
$120
Step 1: Work done by A in 6 days = 6/15 = 2/5. Work done by B in 6 days = 6/20 = 3/10. Step 2: Total work by A and B = 4/10 + 3/10 = 7/10. So, C's work = 3/10. Step 3: C's share = (3/10) * $400 = $120.
597
A, B, and C undertake to do a job for $600. A and C together complete 3/5 of the work. What is B's share?
Answer:
$240
Step 1: The portion of work done by A and C together is 3/5. Step 2: Therefore, B completes the rest, which is 1 - 3/5 = 2/5 of the work. Step 3: B's share = (2/5) * $600 = $240.
598
A, B, and C get a contract for $550. A and B together do 7/11 of the work. How much does C get?
Answer:
$200
Step 1: Since A and B do 7/11 of the work, C must do the remaining part. Step 2: C's share of the work is 1 - 7/11 = 4/11. Step 3: C's payment = (4/11) * $550 = $200.
599
A and B take a job for $450. A can do it in 10 days, B in 15 days. With C's assistance, they complete it in 5 days. Find C's share.
Answer:
$75
Step 1: Work done by A in 5 days = 5/10 = 1/2. Work done by B in 5 days = 5/15 = 1/3. Step 2: Work done by C = 1 - (1/2 + 1/3) = 1/6. Step 3: C's share = 1/6 of $450 = $75.
600
A and B undertake a contract for $300. A can do it alone in 8 days, and B in 12 days. With C's help, they finish it in 4 days. What is C's share?
Answer:
$50
Step 1: In 4 days, A does 4/8 = 1/2 of the work. B does 4/12 = 1/3 of the work. Step 2: C does the remaining work: 1 - (1/2 + 1/3) = 1 - 5/6 = 1/6. Step 3: Since wages are distributed based on work done, C's share is 1/6 of $300 = $50.