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
171
A is 20% less efficient than B. If B takes 24 days to complete a piece of work, how many days will A take?
Answer:
30 days
A's efficiency = 80% of B's = 0.8B. Time taken is inversely proportional to efficiency. Time taken by A = Time of B / 0.8 = 24 / 0.8 = 30 days.
172
A is 50% more efficient than B. If A can do a work in 20 days, how many days will B take to do the same work?
Answer:
30 days
A is 150% of B in efficiency. So, Rate of A = 1.5 * Rate of B. Time taken by B = 1.5 * Time taken by A = 1.5 * 20 = 30 days.
173
A is thrice as fast as B. If they finish a job together in 15 days, how many days will B alone take to finish the job?
Answer:
60 days
A = 3B in efficiency. Let B's rate be 1/x, A's rate is 3/x. Combined rate = 4/x = 1/15. So x = 60. B alone takes 60 days.
174
A takes twice as much time as B to finish a piece of work. If they can finish the work together in 14 days, how many days will A alone take to finish it?
Answer:
42 days
If A takes twice the time of B, A's rate is half of B's. Let A's rate be 1/2x, B's rate be 1/x. Together: 1/2x + 1/x = 3/2x = 1/14. 2x = 42. So A takes 2x = 42 days.
175
A can do a work in 30 days and B in 45 days. They work together, but B leaves 5 days before the work is finished. What is the total number of days taken to finish the work?
Answer:
20 days
Let total days be T. A works for T days, B works for T-5 days. (T/30) + ((T-5)/45) = 1. Multiply by 90: 3T + 2(T-5) = 90 => 5T - 10 = 90 => 5T = 100 => T = 20 days.
176
P can do a task in 15 days and Q in 20 days. They work together for 4 days and then Q leaves. P finishes the remaining work. How many days in total did P work?
Answer:
12 days
P and Q's combined rate = 1/15 + 1/20 = 7/60. In 4 days, they do 28/60 = 7/15. Remaining = 8/15. P takes (8/15)/(1/15) = 8 days to finish. Total days P worked = 4 + 8 = 12 days.
177
A, B, and C can do a piece of work in 10, 12, and 15 days respectively. They started the work together, but A left after 2 days. In how many days will B and C finish the remaining work?
Answer:
3 1/3 days
All three's 1 day work = 1/10+1/12+1/15 = 1/4. In 2 days, they did 2/4 = 1/2 work. Remaining = 1/2. B+C rate = 1/12+1/15 = 9/60 = 3/20. Time = (1/2) / (3/20) = 10/3 = 3 1/3 days.
178
A can finish a work in 10 days and B in 15 days. They start together, but A leaves 5 days before the completion of the work. How many days did the work take to complete?
Answer:
9 days
Let total days be T. A works for T-5 days, B works for T days. ((T-5)/10) + (T/15) = 1. Multiply by 30: 3(T-5) + 2T = 30 => 5T - 15 = 30 => 5T = 45 => T = 9 days.
179
A and B can do a work in 12 and 15 days respectively. They began the work together, but B left 3 days before the completion of the work. In how many days was the total work completed?
Answer:
8 days
Let total days be T. A works for T days, B works for T-3 days. (T/12) + ((T-3)/15) = 1. Multiply by 60: 5T + 4(T-3) = 60 => 9T - 12 = 60 => 9T = 72 => T = 8 days.
180
X can do a job in 20 days and Y in 30 days. They work together for 4 days, after which X leaves. In how many days will Y finish the remaining work?
Answer:
20 days
Combined rate = 1/20 + 1/30 = 1/12. In 4 days, they do 4*(1/12) = 1/3. Remaining work = 2/3. Y's rate is 1/30. Time for Y = (2/3) / (1/30) = 20 days.