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1. A man completes a certain journey by a car. If he covered 30% of the distance at the speed of 20kmph. 60% of the distance at 40km/h and the remaining of the distance at 10 kmph, his average speed is:

A. 25 km/h

B. 28 km/h

C. 30 km/h

D. 33 km/h

Solution:

\begin{aligned} Let the total distance be 100 km . \\ Average speed \\ = \frac{total distance covered}{time taken} \\ = \frac{100}{\frac{30}{20} + \frac{60}{40} + \frac{10}{10}} \\ = \frac{100}{\frac{3}{2} + \frac{3}{2} + 1} \\ = \frac{100}{\frac{3 + 3 + 2}{2}} \\ = \frac{100 \times 2}{8} \\ = 25 kmph \end{aligned}

Alternate
Speed Time and Distance mcq solution image

10% of journey's = 40 km
Then, total journey = 400 kms

\begin{aligned} And, Average speed \\ = \frac{Total distance}{Total time} \\ 30 % of journey \\ = 400 \times \frac{30}{100} \\ = 120 km \\ 60 % of journey \\ = 400 \times \frac{60}{100} \\ = 240 km \\ 10 % of journey \\ = 400 \times \frac{10}{100} \\ = 40 km \\ Average speed \\ = \frac{400}{\frac{120}{20} + \frac{240}{40} + \frac{40}{10}} \\ = \frac{400}{6 + 6 + 4} \\ = \frac{400}{16} \\ ∴ Average speed = 25 km/hr \end{aligned}

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