time and distance Model Questions & Answers, Practice Test for ssc cgl tier 1 2023

Question :1

A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot at the rate of 4 km/hr and partly on bicycle at rate of 9 km/hr. The distance travelled on foot is

Answer: (d)

Let distance travelled on foot = x km

∴ $x/4+{61-x}/9=9$

9x+244-4x=324

5x=80

x=16km

∴ Distance travelled on foot = 16 km

Question :2

A train takes 5 seconds to pass an electric pole. If the length of the train is 120 metres, the time taken by it to cross a railway platform 180 metres long is _______ seconds.

Answer: (c)

Speed of the train = ${120}/5$ = 24 m/s

∴ time taken by the train to pass the platform

= ${120 + 180}/{24}$ = 12.5 seconds

Question :3

A train running between two stations A and B arrives at its destination 10 minutes late when its speed is 50 km/h and 50 minutes late when its speed is 30km/h. What is the distance between the stations A and B ?

Answer: (a)

Let the distance between the two stations be x km.

Then, $x/50-10/60=x/30-50/60$

⇒ $x/50-1/6=x/30-5/6$

or $x/30-x/50=2/3$ or x = 50km

Thus distance between the station A and B = 50 km

Question :4

The speed of a car increases by 2 kilometer after every one hour. If the distance travelled in the first one hour was 35 kilometers, then the total distance travelled in 12 hours was

Answer: (a)

Distance travelled per H = 35,37, 39

$S_n=n/2{[2a+(n-1)d]}$

n=12, a=35, d=2

=$12/2{[2×35+(12-1)×2]}$

=6[70+22]

=6×92=552km.

Question :5

The current of a stream runs at the rate of 4 km an hour. A boat goes 6 km back to the starting point in 2 hours. The speed of the boat in still water is ________ km/hr.

Answer: (b)

Let the speed of boat in still water = x km/hr

Speed of current = 4 km/hr.

Speed upstream = (x – 4) km/hr

Speed downstream = (x + 4) km/hr

Now, $6/{x - 4} + 6/{x + 4}$ = 2

or, ${6(x + 4)(x - 4)}/{x^2 - 16}$ = 2

$2x^2 - 32 = 6x + 6x$

or, $x^2$ – 6x – 16 = 0

or, (x – 8) (x + 2) = 0

∴ x = 8 or – 2.

We reject the negative value.

∴ Speed of boat in still water = 8 km/hr

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