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
651
A can complete a project in 14 days and B in 21 days. They begin together, but A leaves after 3 days. Find the time B takes to finish the remaining work.
Answer:
13.5 days
Step 1: Total work = 42. A's eff = 3, B's eff = 2. Combined eff = 5. Step 2: Work in 3 days = 5 * 3 = 15. Remaining work = 42 - 15 = 27. Step 3: Time taken by B = 27 / 2 = 13.5 days.
652
A can do a piece of work in 15 days, and B can do it in 25 days. They work together for 5 days before B leaves. How many days does A take to finish the rest of the work?
Answer:
7 days
Step 1: Total work = LCM(15, 25) = 75. A's eff = 5, B's eff = 3. Combined = 8. Step 2: Work in 5 days = 8 * 5 = 40. Remaining work = 75 - 40 = 35. Step 3: Time for A = 35 / 5 = 7 days.
653
A can finish a task in 20 days and B in 30 days. They work together for 4 days, after which B leaves. How long will A take to finish the remaining task?
Answer:
13.33 days
Step 1: Total work = 60. A's eff = 3, B's eff = 2. Combined eff = 5. Step 2: Work done in 4 days = 5 * 4 = 20 units. Remaining work = 60 - 20 = 40 units. Step 3: Time taken by A = 40 / 3 = 13.33 days.
654
A can do a job in 12 days and B in 18 days. They start together, but A leaves after 3 days. How many days will B take to complete the remaining job?
Answer:
10.5 days
Step 1: Total work = LCM(12, 18) = 36. A's eff = 3, B's eff = 2. Combined eff = 5. Step 2: Work done in 3 days = 5 * 3 = 15 units. Remaining work = 36 - 15 = 21 units. Step 3: Time taken by B for remaining work = 21 / 2 = 10.5 days.
655
A can do a work in 10 days and B in 15 days. They start together but A leaves after 2 days. How long will B alone take to finish the remaining work?
Answer:
10 days
Step 1: Total work = LCM(10, 15) = 30. A's eff = 3, B's eff = 2. Combined eff = 5. Step 2: Work done in first 2 days = 5 * 2 = 10 units. Remaining work = 30 - 10 = 20 units. Step 3: Time taken by B to finish remaining work = 20 / 2 = 10 days.
656
M is twice as efficient as N. If N takes 24 days to finish a job alone, how many days will M and N take working together?
Answer:
8 days
Step 1: Efficiency ratio M:N = 2:1. Step 2: Total work = N's efficiency * N's time = 1 * 24 = 24 units. Step 3: Combined efficiency = 3. Time taken together = 24 / 3 = 8 days.
657
P is 4 times as fast as Q. They complete a work together in 16 days. In how many days can P alone finish the work?
Answer:
20 days
Step 1: Efficiency ratio P:Q = 4:1. Total efficiency = 5 units/day. Step 2: Total work = 5 * 16 = 80 units. Step 3: Time taken by P alone = Total work / P's efficiency = 80 / 4 = 20 days.
658
A and B together can do a piece of work in 12 days. If A is twice as fast as B, how long will B take alone to complete the work?
Answer:
36 days
Step 1: Efficiency ratio A:B = 2:1. Total efficiency = 3 units/day. Step 2: Total work = Combined efficiency * time = 3 * 12 = 36 units. Step 3: Time taken by B = Total work / B's efficiency = 36 / 1 = 36 days.
659
X is 60% more efficient than Y. If Y alone can do a work in 40 days, how long will X alone take?
Answer:
25 days
Step 1: Efficiency ratio of X:Y = 160:100 = 8:5. Step 2: Total work = Y's efficiency * Y's time = 5 * 40 = 200 units. Step 3: Time taken by X = Total work / X's efficiency = 200 / 8 = 25 days.
660
A is 20% more efficient than B. If A alone finishes a work in 30 days, in how many days can B alone finish it?
Answer:
36 days
Step 1: Efficiency of A to B is 120:100, or 6:5. Step 2: Total work = A's efficiency * A's time = 6 * 30 = 180 units. Step 3: Time taken by B = Total work / B's efficiency = 180 / 5 = 36 days.