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
181
A man walks at 5 km/hr for 6 hours and at 4 km/hr for 12 hours. His average speed is:
Answer:
4.33 km/hr
Total distance = (5 * 6) + (4 * 12) = 30 + 48 = 78 km. Total time = 6 + 12 = 18 hours. Average speed = Total Distance / Total Time = 78 / 18 = 13 / 3 = 4.33 km/hr.
182
A and B start simultaneously from a certain point in opposite directions on a straight path. Their speeds are 3 km/hr and 4 km/hr respectively. In how many hours will they be 35 km apart?
Answer:
5 hours
Since they travel in opposite directions, their relative speed is the sum of their speeds. Relative speed = 3 + 4 = 7 km/hr. Time = Distance / Relative Speed = 35 / 7 = 5 hours.
183
Two boys starting from the same place walk at a rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 8.5 km apart, if they walk in the same direction?
Answer:
17 hours
Relative speed since they walk in the same direction = 5.5 - 5 = 0.5 km/hr. To be 8.5 km apart, the time required = Distance / Relative Speed = 8.5 / 0.5 = 17 hours.
184
A motorboat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is:
Answer:
5 km/hr
Let stream speed be x. 30/(15+x) + 30/(15-x) = 4.5. 30(15-x + 15+x) / (225 - x^2) = 4.5. 900 / (225 - x^2) = 4.5. 225 - x^2 = 200. x^2 = 25 => x = 5 km/hr.
185
A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
Answer:
4 hours
Downstream speed = Speed of boat + Speed of stream = 13 + 4 = 17 km/hr. Time = Distance / Speed = 68 / 17 = 4 hours.
186
In a 100 m race, A can beat B by 10 m and C by 28 m. In a race of 90 m, by what distance will B beat C?
Answer:
18 m
When A covers 100m, B covers 90m and C covers 72m. This means B and C's speeds are in the ratio 90 : 72 = 5 : 4. In a 90m race, when B covers 90m, C will cover 90 * (4/5) = 72m. So, B beats C by 90 - 72 = 18 meters.
187
A man covers a distance of 1200 km in 70 days resting 9 hours a day. If he rests 10 hours a day and walks with speed 1½ times of the previous in how many days will he cover 840 km?
Answer:
35 days
Originally, he travels 24 - 9 = 15 hours a day. Total time = 70 * 15 = 1050 hours. Original speed = 1200 / 1050 = 8/7 km/hr. New speed = 1.5 * (8/7) = 12/7 km/hr. New distance = 840 km. Time required = 840 / (12/7) = 490 hours. Now he rests 10 hours a day, so he travels 14 hours a day. Number of days = 490 / 14 = 35 days.
188
Without stoppages, the speed of a train is 50 km/hr and with stoppages, it is 40 km/hr. For how many minutes does the train stop per hour?
Answer:
12 minutes
Stoppage time per hour = [(Speed without stoppages - Speed with stoppages) / Speed without stoppages] * 60 minutes. Time = [(50 - 40) / 50] * 60 = (10 / 50) * 60 = 12 minutes.
189
Two cars A and B travel from one city to another, at speeds of 35 km/hr and 45 km/hr respectively. If car B takes 2 hours less than car A for the journey, what is the distance between the two cities?
Answer:
315 km
Let the distance be D. The time difference is 2 hours. D/35 - D/45 = 2. LCM of 35 and 45 is 315. (9D - 7D)/315 = 2 => 2D/315 = 2 => D = 315 km. The distance is 315 km.
190
A policeman spots a thief at a distance of 200 meters. The thief starts running and the policeman chases him. If their speeds are 10 km/hr and 12 km/hr respectively, what is the distance the thief ran before being caught?
Answer:
1 km
Relative speed = 12 - 10 = 2 km/hr. Gap to close = 200 m = 0.2 km. Time to catch = 0.2 / 2 = 0.1 hours. Distance covered by thief in this time = Speed * Time = 10 * 0.1 = 1 km = 1000 meters.