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Time and Distance - Aptitude Questions and Answers - RejinpaulPlacement




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1.
How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr? [Bank P.O. 2000]
Answer & Solution
Answer: b) 1   1/5 min

Solution:   Aditya’s speed = 20 km/hr
= [20 * (5/18)] m/sec
= 50/9 m/sec.

Tme taken to cover 400 m = [400 * (9/50)] sec
= 72 sec = 1    12/60 min = 1   1/5 min.
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2.
A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist?
Answer & Solution
Answer: b) 18 km/hr

Solution:   Speed = (750/150) m/sec = 5 m/sec
= [5 * (18/5)] km/hr = 18 km/hr.
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3.
A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds.
Answer & Solution
Answer: c) 16 : 15

Solution:   Let the distance covered in 1 leap of the dog be x and that covered in 1 leap of the hare be y.

Then, 3x = 4y
=> x = 4/3 y
=> 4x = 16/3 y.

Ratio of speeds of dog and hare = Ratio of distance covered by them in the same time
= 4x : 5y
= 16/3 y : 5y = 16/3 : 5 = 16 : 15
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4.
While covering a distance of 24 km, a man noticed that after walking for 1 hour and 40 minutes, the distance covered by him was 5/7 of the remaining distance. What was his speed in metres per second? [R.R.B. 2002]
Answer & Solution
Answer: c) 1   2/3 m/sec.

Solution:   Let the speed be x km/hr.

Then, distance covered in 1 hr 40 min i.e., 1   2/3 hrs = 5x/3 km.

Remaining distance = [24 - (5x/3)] km.
5x/3 = 5/7 [24 - (5x/3)]
=> 5x/3 = 5/7 [(72 - 5x) / 3]
=> 7x = 72 - 5x
=> 12x = 72
=> x = 6

Hence, Speed = 6 km/hr = [6 * (5/18)] m/sec = 5/3 m/sec = 1   2/3 m/sec.
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5.
Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance.
Answer & Solution
Answer: d) 6

Solution:   Let the total distance be x km.

Then, [(2/3)x / 4] + [(1/3)x/5] = 7/5
=> (x/6) + (x/15) = 7/5
=> 7x = 42
=> x = 6
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6.
A man travelled from the village to the post-office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office form the village. [S.S.C 2004]
Answer & Solution
Answer: c) 20 km.

Solution:   Average speed = 2xy / (x+y) km/hr
= (2 * 25 * 4) / (25 + 4) km/hr = 200/29 km/hr.

Distance travelled in 5 hours 48 minutes i.e., 5   4/5 hrs = (200/29 * 29/5) km = 40 km.

Distance of the post-office from the village = (40/2) = 20 km.
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7.
An aeroplane flies along the four sides of a square at the speeds of 200, 400, 600 and 800 km/hr. Find the average speed of the plane around the field.
Answer & Solution
Answer: c) 384 km/hr.

Solution:   Let each side of the square be x km and let the average speed of the plane around the field be y km/hr.

Then, x/200 + x/400 + x/600 + x/800 = 4x/y
=> 25x/2400 = 4x/y
=> y = (2400 * 4)/25 = 384.

Average speed = 384 km/hr.
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