Question

Naresh Kumar drives his car to his office with the speed of 40 Km per hour and returns along the same route with the speed of 60 Km per hour. His average speed for the entire round trip is
A. 50 Km per hour
B. 48 Km per hour
C. 45 Km per hour
D. None of these

Answer 1

Hint: Here we use the formula of Speed to write the time in terms of distance travelled and speed and calculate the total distance and total time. Then we find the average speed using the formula of speed.
* Speed \[ = \]Distance divided by time.
So we can say that Time \[ = \]Distance divided by speed.

Complete step-by-step answer:
Speed of the car when Naresh Kumar goes to the office is 40 Km per hour.
Let the distance travelled by Naresh Kumar be x units and time taken be \[{T_1}\].
\[ \Rightarrow 40 = \dfrac{x}{{{T_1}}}\]
Cross multiplying the values we get
\[ \Rightarrow {T_1} = \dfrac{x}{{40}}\] … (1)
Speed of the car when Naresh Kumar returns from the office is 60 Km per hour.
Let the distance travelled by Naresh Kumar be x units(because the distance between the office and Naresh Kumar’s place is the same) and time taken be \[{T_2}\].
\[ \Rightarrow 60 = \dfrac{x}{{{T_2}}}\]
Cross multiplying the values we get
\[ \Rightarrow {T_2} = \dfrac{x}{{60}}\] … (2)
So for the complete round trip Naresh Kumar travels to the office and comes back.
Total distance \[ = x + x\]
Total distance \[ = 2x\]
Total time taken \[ = {T_1} + {T_2}\]
Substitute the values from equation (1) and (2)
Total time taken \[ = \dfrac{x}{{40}} + \dfrac{x}{{60}}\]
Take LCM on RHS.
\[ \Rightarrow \]Total time taken \[ = \dfrac{{60x + 40x}}{{40 \times 60}}\]
\[ \Rightarrow \]Total time taken \[ = \dfrac{{100x}}{{2400}}\]
\[ \Rightarrow \]Total time taken \[ = \dfrac{x}{{24}}\]
So, the average speed can be calculated by dividing total distance travelled by total time taken.
\[ \Rightarrow \]Average speed\[ = \dfrac{{2x}}{{\dfrac{x}{{24}}}}\]
\[ \Rightarrow \]Average speed \[ = \dfrac{{2x \times 24}}{x}\]
Cancel the same terms from numerator and denominator.
\[ \Rightarrow \]Average speed \[ = 48\]Km per hour

So, the correct option is B.

Note: Students are likely to make mistake of calculating the average speed by taking average of the two given speed like \[\dfrac{{40 + 60}}{2} = 50\] which is wrong because that will be the average of the speeds given and not the average speed for the whole round trip.