Test: Speed, Time & Distance (March 11) - CAT MCQ

It is given in the question that a man crosses 600m long street in 5 minutes. We have to find the speed of the man in km per hour. To find the speed of the man in km per hour, we have to convert the given distance to km and also convert the given time to hour.
First, let us see the conversion of the given distance into km. We know that 1km = 1000m.
So, to convert 600m to km, we can write, 600m = x km.
x = 600/1000 km 
x = 0.6km 
Now, let us convert the given time into hours. We know that 1 hour = 60 minutes.
So, to convert 5 minutes to hours, we can write, 5 minutes = y hours.
y = 5/60 hrs
y = 0.083 hrs
Now we know that speed can be found out using the formula, Speed=Distance/Time, We have found out that distance = 0.6km and time = 0.083 hrs. So, on substituting these values in the formula of speed, we get,  
Speed = 0.6/ 0.083
= 6×1000 / 83 × 10
= 6000/ 830
= 600/83
= 7.2 km/h
Therefore, we get the speed of the man crossing a 600m long street in 5 minutes as 7.2km/h.
Hence, option (D) is the correct answer.

Let the distance be x km. Then,
(Time taken to walls x km) + (Time taken to ride x km) = 23/4 hrs
⇒  (Time taken to walls 2x km) + Time taken to ride 2x km  =  23/2 hrs
but time taken to ride 2x km = 15/4 hrs 
Therefore, Time taken to walk 2x km = (23/2 - 15/4) hrs = 31/4 hrs =7 hr 45 min.

It is given that, excluding stoppages, the speed of a bus is 54 kmph.
⇒ Distance travelled by bus in 1 hour, excluding stoppages = 54 km.
Also, it is given that including stoppages the speed of the bus is 45 km/hr.
⇒ Distance travelled by the bus in 1 hour, including stoppages = 45 km.
(Distance travelled by bus in 1 hour excluding stoppages – distance travelled by bus in 1 hour including stoppages)
⇒ (54km−45km) ⇒ 9 km
Due to stoppages, it covers 9 km less in an hour.
Students can easily solve this question by using this trick.
Required time for the stoppage per hour,

Let time taken to travel the first half = x hr 
⇒ Time taken to travel the second half = (10 - x) hr 

∵ Distance = Time * Speed
Distance covered in the first half = 21x 
Distance covered in the the second half = 24(10 - x)

∵  Distance covered in the the first half = Distance covered in the the second half
⇒ 21x = 24(10 - x)
⇒ 45x = 240
⇒ x = 16/3

Total Distance = 2 * 21(16/3) = 224 Km [∵ multiplied by 2 as 21x was the distance of half way]

Time taken = 1 hr 40 min 48 sec = 1 hr (40 + 4/5) min = 1 + 51/75 hrs = 126/75 hrs
Let the actual speed be x km/hr
Then, (5/7) * x * (126/75) = 42
⇒ x = 42 * 7 * (75 / 5) * 126
⇒ x = 35 km/hr

Relative speed = Speed of A + Speed of B = 2 + 3 = 5 rounds per hour
(∴ they walk in opposite directions)

⇒ They cross each other 5 times in 1 hour and 2 times in 1/2 hour

∵ Time duration from 8 a.m. to 9.30 a.m. = 1.5 hour

∴ They cross each other 7 times before 9.30 a.m

In this type of question, we need to get the relative speed between them.

The relative speed of the boys = 5.5 – 5 = 0.5 km/h

The distance between them is 8.5 km.
Time = Distance/Speed
Time = 8.5/0.5 = 17 hrs

Let Anil takes x hrs.
⇒ Arun takes x+2

If Arun doubles the speed, he will take x-1 hrs
⇒ He needs 3 hours less.
∵ Double speed means half time.
∴ Half of the time required by Arun to cover 30 km = 3 hours

⇒ Time required by Arun to cover 30 km = 6 hour
Thus, Arun's speed = 30/6 = 5 km/h

Total time taken = (160/64) + (160/80) = 9/2 hrs
∴ Average speed = 320 x (2/9) = 71.11 km/hr.