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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

Answer: c
Explanation: Let distance be 120 km
Hence 30 km is covered by 25 kmph and 40 km covered by 30 kmph and rest 50 km has been covered 50 kmph
$$\eqalign{ & {\text{average}} = {\frac{{120}}{{{\text{total}}\,{\text{time}}\,{\text{taken}}}}} \cr & = \frac{{120}}{{\frac{{30}}{{25}} + \frac{{40}}{{30}} + \frac{{50}}{{50}}}} \cr & = \frac{{3600}}{{106}} \cr & = \frac{{1800}}{{53}}\,{\text{km/h}} \cr} $$

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