# Time Speed and Distance Questions for CAT

CAT 2020 MOCK Test Series at INR 1000/- only.
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?
 110 sec
 99 sec
 88 sec
 11 sec

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
 20 kmph
 25 kmph
 30 kmph
 50 kmph

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.
 7.5 m
 750 km
 7.5 km
 15 km

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.
 40.2 kmph
 31.2 kmph
 50.3 kmph
 36 kmph

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
 15 km
 2 km
 10 km
 30 km

. By a previously explained logic, $x/10 - x/15 = 1/2$
$\Rightarrow X = 15km$