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
211
A train 100 meters long is running at a speed of 36 km/hr. How much time will it take to pass a stationary man?
Answer:
10 seconds
First, convert the speed of the train from km/hr to m/s. Speed = 36 * (5/18) = 10 m/s. Since a stationary man has negligible length, the distance to be covered is just the length of the train (100 m). Time = Distance / Speed = 100 / 10 = 10 seconds.
212
A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time, what should be his speed in km/hr to cover the remaining distance in the remaining time?
Answer:
12 km/hr
Total distance = 6 km, Total time = 45 minutes = 3/4 hours. Remaining distance = 6 / 2 = 3 km. Remaining time = 1/3 of total time = 1/3 * 45 = 15 minutes = 1/4 hours. Required speed = Remaining Distance / Remaining Time = 3 / (1/4) = 12 km/hr.
213
A train covers a distance in 50 minutes if it runs at a speed of 48 km/hr on average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.
Answer:
60 km/hr
First, find the total distance. Distance = Speed * Time = 48 * (50/60) = 40 km. To cover this distance in 40 minutes (which is 40/60 hours), the new speed = Distance / New Time = 40 / (40/60) = 40 * (60/40) = 60 km/hr.
214
By walking at 4 km/hr, a person reaches his office 15 minutes late. If he walks at 6 km/hr, he reaches 10 minutes early. What is the distance to the office?
Answer:
5 km
Time difference = 15 mins late + 10 mins early = 25 minutes = 25/60 hours = 5/12 hours. Distance = [Product of speeds / Difference of speeds] * Time difference = [(4 * 6) / (6 - 4)] * (5/12) = [24 / 2] * (5/12) = 12 * (5/12) = 5 km.
215
A man covers a certain distance on a scooter. Had he moved 3 km/hr faster, he would have taken 40 minutes less. If he had moved 2 km/hr slower, he would have taken 40 minutes more. Find the distance.
Answer:
40 km
Using the formula: Distance = [S1 * S2 / (S1 - S2)] * Time difference. Let usual speed be S. Distance = [S*(S+3)/3] * (40/60) and Distance = [S*(S-2)/2] * (40/60). Equating the two: S(S+3)/3 = S(S-2)/2. 2S + 6 = 3S - 6 => S = 12 km/hr. Distance = [12 * 15 / 3] * (2/3) = 60 * (2/3) = 40 km.
216
If a student walks from his house to school at 4 km/hr, he is late by 10 minutes. If he walks at 5 km/hr, he reaches 5 minutes early. Find the distance to his school.
Answer:
5 km
Let the distance be D. The difference in time taken at the two speeds is 15 minutes (10 mins late + 5 mins early = 15 mins = 1/4 hour). So, D/4 - D/5 = 1/4. Solving this, (5D - 4D)/20 = 1/4 => D/20 = 1/4 => D = 5 km.
217
A person travels a distance of 100 km at a speed of 25 km/hr and another 150 km at 50 km/hr. What is the average speed for the whole journey?
Answer:
35.7 km/hr
Total Distance = 100 + 150 = 250 km. Time for the first part = 100 / 25 = 4 hours. Time for the second part = 150 / 50 = 3 hours. Total time = 4 + 3 = 7 hours. Average speed = 250 / 7 ≈ 35.71 km/hr.
218
A train covers the first half of the distance at 50 km/hr and the second half at 70 km/hr. Find its average speed.
Answer:
58.3 km/hr
Since the distances are equal, we use the formula for average speed: (2 * S1 * S2) / (S1 + S2). Average speed = (2 * 50 * 70) / (50 + 70) = 7000 / 120 = 58.33 km/hr.
219
A man divides his journey into three equal parts and travels at speeds of 20, 30, and 60 km/hr. What is his average speed?
Answer:
30 km/hr
For three equal distances covered at speeds a, b, and c, the average speed is 3abc / (ab + bc + ca). Average speed = (3 * 20 * 30 * 60) / (600 + 1800 + 1200) = 108000 / 3600 = 30 km/hr. Alternatively, assuming each distance part is 60 km, total distance = 180 km, total time = 3 + 2 + 1 = 6 hours, Average speed = 180/6 = 30 km/hr.
220
A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. What is his average speed for the entire trip?
Answer:
10.8 km/hr
Total Distance = 10 + 12 = 22 km. Time taken for the first part = 10/12 = 5/6 hours. Time for the second part = 12/10 = 6/5 hours. Total time = 5/6 + 6/5 = (25 + 36)/30 = 61/30 hours. Average speed = Total Distance / Total Time = 22 / (61/30) = 660 / 61 ≈ 10.8 km/hr.