A car travels from P to Q at 30 km/h and returns at 45 km/h. What is its average speed for the round trip?
Solution
For equal distances, average speed = 2ab/(a + b) = 36 km/h.
Answer: (C) 36 km/h
Quantitative Aptitude · Work and motion
Time, Speed and Distance: MAH CET, NMAT and SNAP practice questions
20 questions in the pattern of MAH MBA CET, NMAT and SNAP. Each question is marked with the exams it suits. Answer it, then open the step-by-step solution.
Exam:
Two runners start together from the same point on a 1200 m circular track and run in the same direction at 4 m/s and 8 m/s. After how many seconds will they first meet?
Solution
Relative speed = |4 − 8| = 4 m/s.
Time = 1200/4 = 300 s.
Answer: (B) 300 seconds
An athlete runs at 30 m/s. What is this speed in km/h?
Solution
Multiply by 18/5: 30 × 18/5 = 108 km/h.
Answer: (C) 108 km/h
Two towns are 180 km apart. Two cars start from them at the same time towards each other at 30 km/h and 60 km/h. After how long will they meet?
Solution
Relative speed = 90 km/h.
Time = 180/90 = 2 hours.
Answer: (D) 2 hours
A thief runs away in a car at 45 km/h. The police start 120 minutes later at 69 km/h. How long after the police start will they catch the thief?
Solution
Head start = 45 × 2 = 90 km.
Relative speed = 24 km/h, so time = 90/24 = 3.75 hours.
Answer: (A) 3.75 hours
If a car had gone 10 km/h faster, it would have taken 1 hour less to cover 120 km. What is its actual speed?
Solution
120/v − 120/(v + 10) = 1.
Trying the options, v = 30 works: 4 − 3 = 1.
Answer: (D) 30 km/h
A man covers three equal distances of 120 km each at 40, 30 and 60 km/h. What is his average speed?
Solution
Total time = 120/40 + 120/30 + 120/60 = 9 h.
Average speed = 360/9 = 40 km/h.
Answer: (C) 40 km/h
The speeds of A and B are in the ratio 6 : 5. If A takes 20 minutes to cover a distance, how long will B take?
Solution
For a fixed distance, time ∝ 1/speed, so time ratio = 5 : 6.
B's time = 20 × 6/5 = 24 minutes.
Answer: (B) 24 minutes
Walking at 2/3 of his usual speed, a man is 15 minutes late. What is his usual time for the journey?
Solution
At 2/3 speed, time becomes 3/2 of usual: (3/2 − 1)T = 15.
T = 30 minutes.
Answer: (B) 30 minutes
Travelling at 60 km/h a man reaches office 10 minutes late; at 75 km/h he reaches 10 minutes early. How far is his office?
Solution
The two times differ by 20 minutes: d/60 − d/75 = 20/60.
d = 1/3 × 60 × 75/15 = 100 km.
Answer: (A) 100 km
A car covers 300 km at 30 km/h. How many minutes would it save if it travelled 20 km/h faster?
Solution
Time at 30 km/h = 10 h; at 50 km/h = 6 h.
Saved = 4 h = 240 minutes.
Answer: (D) 240 minutes
The speeds of A and B are in the ratio 6 : 5. If A takes 60 minutes to cover a distance, how long will B take?
Solution
For a fixed distance, time ∝ 1/speed, so time ratio = 5 : 6.
B's time = 60 × 6/5 = 72 minutes.
Answer: (D) 72 minutes
A man travels 1/3 of a 120 km journey at 60 km/h and the rest at 30 km/h. What is his average speed?
Solution
Time = 40/60 + 80/30 = 3 1/3 hours.
Average speed = 120/3 1/3 = 36 km/h.
Answer: (C) 36 km/h
A thief runs away in a car at 40 km/h. The police start 60 minutes later at 60 km/h. How long after the police start will they catch the thief?
Solution
Head start = 40 × 1 = 40 km.
Relative speed = 20 km/h, so time = 40/20 = 2 hours.
Answer: (C) 2 hours
An athlete runs at 25 m/s. What is this speed in km/h?
Solution
Multiply by 18/5: 25 × 18/5 = 90 km/h.
Answer: (B) 90 km/h
A man covers three equal distances of 60 km each at 30, 60 and 40 km/h. What is his average speed?
Solution
Total time = 60/30 + 60/60 + 60/40 = 4.5 h.
Average speed = 180/4.5 = 40 km/h.
Answer: (A) 40 km/h
Without stoppages a bus runs at 50 km/h; with stoppages its average speed is 35 km/h. For how many minutes per hour does the bus stop?
Solution
It loses 15 km per hour because of stops.
Stop time per hour = 15/50 × 60 = 18 minutes.
Answer: (B) 18 minutes
Travelling at 40 km/h a man reaches office 12 minutes late; at 60 km/h he reaches 5 minutes early. How far is his office?
Solution
The two times differ by 17 minutes: d/40 − d/60 = 17/60.
d = 17/60 × 40 × 60/20 = 34 km.
Answer: (B) 34 km
Without stoppages a bus runs at 40 km/h; with stoppages its average speed is 25 km/h. For how many minutes per hour does the bus stop?
Solution
It loses 15 km per hour because of stops.
Stop time per hour = 15/40 × 60 = 22.5 minutes.
Answer: (C) 22.5 minutes
Walking at 3/5 of his usual speed, a man is 20 minutes late. What is his usual time for the journey?
Solution
At 3/5 speed, time becomes 5/3 of usual: (5/3 − 1)T = 20.
T = 30 minutes.
Answer: (A) 30 minutes
These are original practice questions written by Target Campus in the pattern and difficulty of MAH MBA CET, NMAT, SNAP and other MBA entrance tests. They are not previous-year papers.
Preparing for MAH CET, SNAP or NMAT? Courses, live classes and mocks by Dr. Kiran Derle at Target Campus.
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