A boy goes from his house to school by bus at a speed of $20 k m / h$ and returns back through the same route at a speed of $30 k m / h$ . The average speed of his journey is:

25 km/h

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40 km/h

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20 km/h

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24 km/h

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Solution

The correct option is D $24 km/h$
Let the total distance from the house to the school be x km. The speed of the bus to and from the school is $20 k m / h$ and $30 k m / h$ , respectively. We can calculate the time taken for going to the school and coming back, as follows:

Time taken for going $= x / 20 h$
Time taken for coming back
$= x / 30 h$

Total time taken for the entire journey $= (x / 20 + x / 30) h$
Total distance for the entire journey $= x + x = 2 x$
Formula for average speed = Total distance travelled / Total time taken

Therefore,average speed $= (2 x) / (x / 20 + x / 30)$
$2 x / (5 x / 60) = 24 k m / h$

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A boy goes from his house to school by bus at a speed of 20 km/h and returns back through the same route at a speed of 30 km/h. The average speed of his journey is:

A boy goes from his house to school by bus at a speed of $20 k m / h$ and returns back through the same route at a speed of $30 k m / h$ . The average speed of his journey is: