This set covers time and work, pipes and cisterns, time speed and distance, trains, boats and streams, and averages. These topics are staples of campus placement tests and competitive exams, and every question here comes with a short worked solution.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 18 questions.
Topics covered in this set
- Time and work, efficiency and man-days
- Pipes and cisterns
- Average speed and relative speed
- Problems on trains
- Boats and streams
- Averages
Aptitude MCQs with answers and explanations
Q1. A speed of 72 km/h is equal to:
a) 20 m/s
b) 25 m/s
c) 18 m/s
d) 72 m/s
Q2. A can do a piece of work in 10 days and B can do it in 15 days. In how many days can they finish it working together?
a) 12.5 days
b) 6 days
c) 5 days
d) 8 days
Q3. A and B together can finish a job in 12 days. A alone can finish it in 20 days. How many days will B alone take?
a) 8 days
b) 24 days
c) 30 days
d) 32 days
Q4. 12 men can complete a work in 18 days. In how many days will 27 men complete the same work?
a) 8 days
b) 40.5 days
c) 9 days
d) 6 days
Q5. A is twice as efficient as B, and together they finish a task in 14 days. How many days will A alone take?
a) 28 days
b) 42 days
c) 18 days
d) 21 days
Q6. Pipe A can fill a tank in 20 minutes and pipe B can empty the full tank in 30 minutes. If both are opened together on an empty tank, how long will it take to fill?
a) 12 minutes
b) 50 minutes
c) 60 minutes
d) 10 minutes
Q7. Pipes A and B can fill a tank in 12 hours and 15 hours respectively, while pipe C can empty it in 20 hours. If all three are opened together, in how many hours will the empty tank be filled?
a) 10 hours
b) 8 hours
c) 6.67 hours
d) 12 hours
Q8. A car goes from P to Q at 40 km/h and returns from Q to P at 60 km/h. What is its average speed for the whole journey?
a) 50 km/h
b) 48 km/h
c) 52 km/h
d) 45 km/h
Q9. A train 150 m long is running at 54 km/h. How long will it take to cross an electric pole?
a) 15 seconds
b) 12 seconds
c) 8 seconds
d) 10 seconds
Q10. A train 200 m long running at 72 km/h crosses a platform 300 m long. How much time does it take?
a) 10 seconds
b) 15 seconds
c) 25 seconds
d) 20 seconds
Q11. Two trains of lengths 120 m and 180 m run on parallel tracks in opposite directions at 50 km/h and 40 km/h. How long will they take to cross each other completely?
a) 12 seconds
b) 30 seconds
c) 10.8 seconds
d) 15 seconds
Q12. Two trains 100 m and 150 m long run in the same direction at 68 km/h and 50 km/h. How long will the faster train take to pass the slower one completely?
a) 20 seconds
b) 7.6 seconds
c) 50 seconds
d) 45 seconds
Q13. A boat goes 16 km/h downstream and 10 km/h upstream. What is the speed of the stream?
a) 6 km/h
b) 13 km/h
c) 2.5 km/h
d) 3 km/h
Q14. A boat's speed in still water is 15 km/h and the stream flows at 3 km/h. How long will the boat take to go 36 km downstream and come back?
a) 4.8 hours
b) 5 hours
c) 6 hours
d) 4.5 hours
Q15. A thief is spotted by a policeman from 300 m away. The thief runs at 8 km/h and the policeman chases at 10 km/h. How far will the thief have run before he is caught?
a) 1.5 km
b) 0.3 km
c) 1.2 km
d) 2.4 km
Q16. The average of 5 numbers is 20. If one number is removed, the average of the remaining numbers becomes 18. What is the number removed?
a) 28
b) 2
c) 22
d) 38
Q17. The average age of 30 students in a class is 15 years. When the teacher's age is included, the average increases by 1 year. What is the teacher's age?
a) 31 years
b) 46 years
c) 45 years
d) 16 years
Q18. A batsman scores 85 runs in his 17th innings and thereby increases his average by 3. What is his average after the 17th innings?
a) 34
b) 40
c) 37
d) 38
Quick revision notes
- If A takes a days and B takes b days, together they take ab/(a + b) days.
- Work = men x days (man-days) stays constant for the same job: M1 x D1 = M2 x D2.
- Treat an emptying pipe as negative work: net rate = sum of filling rates - sum of emptying rates.
- km/h to m/s: multiply by 5/18; m/s to km/h: multiply by 18/5.
- Average speed for equal distances at x and y = 2xy/(x + y).
- Relative speed: add speeds for opposite directions, subtract for the same direction.
- Train crossing a pole covers its own length; crossing a platform or another train covers the sum of lengths.
- Boat in still water = (down + up)/2; stream = (down - up)/2.
Frequently asked questions
What is the LCM method in time and work questions?
Take the total work as the LCM of the given days so that every person's daily work becomes a whole number of units. For example, with 10 and 15 days, take 30 units: A does 3 units/day and B 2 units/day, so together 30/5 = 6 days.
Why is average speed not the simple average of the two speeds?
Average speed is total distance divided by total time. When equal distances are covered at different speeds, more time is spent at the slower speed, so the answer is the harmonic mean 2xy/(x + y), which is always less than the simple average.
How do I decide what distance a train covers while crossing something?
The train must move until its tail clears the object. For a pole or a person, the distance is just the train's length; for a platform, bridge or another train, add the lengths together and use the appropriate relative speed.
Comments
Post a Comment