Time Speed and Distance Questions for CAT

Question 6: Two trains 121 m and 99 m in length respectively are running in opposite directions, one at the rate of 40 kmph and the other at the rate of 32 kmph. How long will they take to be completely clear of each other from the moment they meet?
[1] 110 sec
[2] 99 sec
[3] 88 sec
[4] 11 sec

Answer:

Option: 4

Explanation:

Time taken to cover\( = \left( {121 + 99} \right) = 220\)

at the rate of (32 + 40), i.e. 72 kmph = \(\frac{{220}}{{\left( {72 \times \frac{5}{{18}}} \right)}}\)sec =11 sec.


Question 7: A jeep travels a distance of 100 km at a uniform speed. If the speed of the jeep is 5 kmph more, then it takes 1 hour less to cover the same distance. The original speed of the jeep is
[1] 20 kmph
[2] 25 kmph
[3] 30 kmph
[4] 50 kmph

Answer:

Option: 1

Explanation:

Let the original speed of the jeep be x kmph.

\( \Rightarrow \frac{{100}}{x} - \frac{{100}}{{x + 5}} = 1\)

Solving this, we get x = 20 kmph.


Question 8: Two athletes cover the same distance at the rate of 10 and 15 kmph respectively. Find the distance travelled when one takes 15 minutes longer than the other.
[1] 7.5 m
[2] 750 km
[3] 7.5 km
[4] 15 km

Answer:

Option: 3

Explanation:

Let the distance be D km.

\( \Rightarrow \frac{D}{{10}} - \frac{D}{{15}} = \frac{{15}}{{60}} \Rightarrow \frac{D}{{30}} = \frac{1}{4} \Rightarrow D = 7.5km\)


Question 9: A motorcyclist covers 4 successive 4 km stretches at speeds of 20 kmph, 30 kmph, 40 kmph, and 50 kmph respectively. Find the average speed over the total distance.
[1] 40.2 kmph
[2] 31.2 kmph
[3] 50.3 kmph
[4] 36 kmph

Answer:

Option: 2

Explanation:

Average speed =\(\frac{{Total{\rm{ distance covered }}}}{{{\rm{ time taken }}}} = \frac{{16}}{{\frac{4}{{20}} + \frac{4}{{30}} + \frac{4}{{40}} + \frac{4}{{50}}}}\)

\( = \frac{{16 \times 600}}{{120 + 80 + 60 + 48}} = \frac{{9600}}{{308}} = 31.17\) kmph


Question 10: Ram and Shyam travel the same distance at the speeds of 10 kmph and 15 kmph respectively. If Ram takes 30 min longer than Shyam, then the distance travelled is
[1] 15 km
[2] 2 km
[3] 10 km
[4] 30 km

Answer:

Option: 1

Explanation:

. By a previously explained logic, \(x/10 - x/15 = 1/2\)

\( \Rightarrow X = 15km\)



Time Speed and Distance

Time Speed and Distance Questions for CAT
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