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1. One-fourth of certain journey is covered at the rate of 25 km/h, one-third at the rate of 30 km/h and the rest at 50 km/h. Find the average speed for the whole journey.

A. $\frac{600}{53}$ km/h

B. $\frac{1200}{53}$ km/h

C. $\frac{1800}{53}$ km/h

D. $\frac{1600}{53}$ km/h

Solution:

Let distance be 120 kmHence 30 km is covered by @25 kmph and 40 km covered by @30 kmph and rest 50 km has been covered @50 kmph
Now,

\begin{aligned} average = \frac{120}{total time taken} \\ = \frac{120}{\frac{30}{25} + \frac{40}{30} + \frac{50}{50}} \\ = \frac{3600}{106} \\ = \frac{1800}{53} km/h \end{aligned}

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