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A bus is travelling the first one third distance at a speed of $10 km / h$ the next one fourth of the total distance at $20 km / h$ and remaining at $40 km / h$ . What is the average speed of the bus?

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17.78 km / h

28.24 km / h

18 km / h

20 km / h

answer is A.

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Detailed Solution

A bus is travelling the first one third distance at a speed of

10 km / h

the next one fourth of the total distance at

20 km / h

and remaining at

40 km / h

, the average speed of the bus

17.78 km / h

.
Let total distance be

D km

.
One third distance will be

D / 3 km

and time will be

\frac{D}{30} h

.
For next one fourth

(D / 4)

of the total distance’s time will be

\frac{D}{80} h

.
And remaining

5 D / 12

40 km / h

, So time will be

\frac{5 D}{480} h

.
So total time will be,

\frac{D}{30} + \frac{D}{80} + \frac{5 D}{480} = \frac{27 D}{480}

As we know

average speed = \frac{Total distance}{Total time}

so average speed

= \frac{D}{(\frac{27 D}{480})}

= \frac{480}{27}

= 17.78 km / h

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