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
111
P, Q, and R can do a work in 12, 15, and 20 days respectively. They start together, but R leaves after 2 days. How many days will P and Q take to finish the rest?
Answer:
4 days
Step 1: Total work = 60. P's eff = 5, Q's eff = 4, R's eff = 3. Combined eff = 12. Step 2: Work in 2 days = 12 * 2 = 24. Remaining work = 60 - 24 = 36. Step 3: Combined eff of P and Q = 9. Time taken = 36 / 9 = 4 days.
112
A, B, and C can do a work in 10, 20, and 30 days respectively. They all start together, but A leaves after 2 days. How long will B and C take to finish the remaining work?
Answer:
7.6 days
Step 1: Total work = 60. A's eff = 6, B's eff = 3, C's eff = 2. Combined eff = 11. Step 2: Work in 2 days = 11 * 2 = 22. Remaining work = 60 - 22 = 38. Step 3: Combined eff of B and C = 5. Time for B and C = 38 / 5 = 7.6 days.
113
X can do a job in 24 days and Y in 36 days. They start together and X leaves after 4 days. How many days will Y take to finish the remaining job?
Answer:
26 days
Step 1: Total work = 72. X's eff = 3, Y's eff = 2. Combined eff = 5. Step 2: Work done in 4 days = 5 * 4 = 20. Remaining work = 72 - 20 = 52. Step 3: Time taken by Y = 52 / 2 = 26 days.
114
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.
115
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.
116
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.
117
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.
118
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.
119
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.
120
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.