Question

A man takes 150 steps in walking 120 meters. Find his speed in km/hr, if he takes 3 steps in one second.
(a) 8.64 km/hr
(b) 9.39 km/hr
(c) 5.82 km/hr
(d) 4.77 km/hr

Answer 1

Hint: Start by finding the distance walked by man in 3 steps using the point that man walks 120 meters of distance in 150 steps. Divide the result you get by 1 sec, as the man takes 1 sec to take 3 steps. The answer you get is the speed of the man in meters per second. Convert the speed to km per hour using the fact that 1km is equal to 1000 meters and 1 hour is equal to 3600 seconds.

Complete step-by-step answer:
Let us start the solution to the above question by finding the distance walked by man in 3 steps. It is given that the distance travelled by man in 150 steps is 120 meters. So, we can say that the distance travelled by man in 1 step is given by $ \dfrac{120}{150}\text{ meters} $ . Therefore, the distance travelled in 3 steps is equal to $ \dfrac{120}{150}\times \text{3=}\dfrac{12}{5}\text{ meters} $ .
Also, it is given that the man takes 1 sec to take 3 steps and according to the definition of speed, the distance travelled by the object per second is speed, so the speed of the man is $ \dfrac{12}{5}\text{ m/sec} $ .
Now, as all the options are given in km per hour, we will convert the speed we got in km/hr. For converting we will multiply the speed in m/s by 3600 to get the distance covered in 3600 seconds, i.e., 1 hour and divide it by 1000 to convert it to km, the answer you get is the kmph value of the speed that you were having in m/s.
 $ \text{speed of man=}\dfrac{12}{5}\times \dfrac{3600}{1000}\text{ =}\dfrac{216}{25}=8.64\text{ }km/hr $
Therefore, the answer to the above question is option (a).

Note: Don’t forget to convert the elements given in the question to the units which you are asked to report the answer before using them in calculation as we did by converting the answer we get in km/hr, which you can remember as for converting m/s to km/hr multiply the m/s value by $ \dfrac{18}{5} $ .