time and distance Model Questions & Answers, Practice Test for ibps clerk prelims 2023

Question :1

A train speeds past a pole in 15 seconds and speeds past a platform 100 metres long in 25 seconds. Its length in metres is ________ .

Answer: (b)

Let the length of the train = x m

Then, speed of the train = $x/{15} = {x + 100}/{25}$

or, 25x = 15x + 1500 or, 10x = 1500

∴ x = 150 m

Question :2

A boy rows a boat against a stream flowing at 2 kmph for a distance of 9 km, and then turns round and rows back with the current. If the whole trip occupies 6 hours, find the boy's rowing speed in still water.

Answer: (c)

Let the speed of rowing be X. Then the equation formed

is $9/{X-2}+9/{X+2}=6.$

On solving, we get the value of X as 4.

Question :3

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph respectively and passes them completely in 9 and 10 seconds respectively. The length of the train is _________ metres.

Answer: (b)

Let the length of train = x m.

We know that, when train and man are moving in the same direction relative speed = Speed o Train – Speed of Man

∴ Speed of train = Relative speed + Speed of man

Now,

Speed of train in two cases = $x/9 + 2(5/18) = x/{10} + 4(5/18)$

or, $x/9 - x/{10} = {10}/9 - 5/9 or, x/{90} = 5/9$

∴ x = $5/9$ × 90 = 50 m.

Question :4

The wheel of an engine 4$2/7$ metres in circumference makes seven revolutions in 4 seconds. Find the speed of the train in km per hour.

Answer: (c)

Distance covered in 4 seconds = ${30}/7$ × 7 metres

∴ Speed in m/s = ${30}/4$

∴ Speed in km/hr = ${30}/4 × {18}/5$ = 27 km/hr

Question :5

The ratio between the speed of a train and a car is 18 : 13 . Also, a bus covered a distance of 480 kms. in 12 hours. The speed of the bus is five-ninth the speed of the train. How much distance will the car cover in 5 hours ?

Answer: (b)

Speed of bus

= $480/12$ = 40 km/hr

Speed of train

= $40×9/5$ = 72 km/hr

Speed of car

= $72/18×13 = 52$km/hr

Distance covered by car

= 52 × 5 = 260 km

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