Question : Gautam goes to work at a speed of 12 km/hr and returns home at 10 km/hr. His average speed is:
Option 1: 11 km/hr
Option 2: 22 km/hr
Option 3: 10.9 km/hr
Option 4: 12.5 km/hr
Correct Answer: 10.9 km/hr
Solution :
Given:
Gautam goes to work at a speed of 12 km/hr.
He returns home at a speed of 10 km/hr.
Let the distance between home and office be $x$.
Then, the total distance is 2$x$.
Time taken to reach office $=\frac{x}{12}$ hr
Time taken to reach home $=\frac{x}{10}$ hr
Total time to reach office and return home $=\frac{x}{12}+\frac{x}{10} =\frac{5x+6x}{60} =\frac{11x}{60}$ hr
Now, Average speed $= \frac{\text{Total distance}}{\text{Total time}}$
$=\frac{2x}{\frac{11x}{60}}$
$= \frac{2x×60}{11x}$
$= \frac{120}{11}$
= 10.9 km/hr (approx.)
Hence, the correct answer is 10.9 km/hr.
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