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 Answer: Option AShow Answer
Solution(By Apex Team)
$\begin{array}{l}\text{ Let the total distance be 100 km}\\
\begin{array}{l}\text{ Average speed }\\
=\frac{\text{ total distance covered }}{\text{ time taken }}\\
=\frac{100}{\frac{30}{20}+\frac{60}{40}+\frac{10}{10}}\\
=\frac{100}{\frac{3}{2}+\frac{3}{2}+1}\\
=\frac{100}{3+3+2}\\
=\frac{100\times2}{8}\\
=25\mathrm{kmph}\end{array}\end{array}$
$\begin{array}{l}\text{ And, Average speed }\\
=\frac{\text{ Total distance }}{\text{ Total time }}\\
30\%\text{ of journey }\\
=400\times\frac{30}{100}\\
=120\mathrm{~km}\\
60\%\text{ of journey }\\
=400\times\frac{60}{100}\\
=240\mathrm{~km}\\
10\%\text{ of journey }\\
=400\times\frac{10}{100}\\
=40\mathrm{~km}\\
\text{ Average speed }\\
=\frac{400}{\frac{120}{20}+\frac{240}{40}+\frac{40}{10}}\\
=\frac{400}{6+6+4}\\
=\frac{400}{16}\\
\therefore\text{ Average speed }=25\mathrm{\ km}\end{array}$
Alternate Solution:
10% of journey’s = 40 km Then, total journey = 400 kms
$\begin{array}{l}\text{ And, Average speed }\\
=\frac{\text{ Total distance }}{\text{ Total time }}\\
30\%\text{ of journey }\\
=400\times\frac{30}{100}\\
=120\mathrm{~km}\\
60\%\text{ of journey }\\
=400\times\frac{60}{100}\\
=240\mathrm{~km}\\
10\%\text{ of journey }\\
=400\times\frac{10}{100}\\
=40\mathrm{~km}\\
\text{ Average speed }\\
=\frac{400}{\frac{120}{20}+\frac{240}{40}+\frac{40}{10}}\\
=\frac{400}{6+6+4}\\
=\frac{400}{16}\\
\therefore\text{ Average speed }=25\mathrm{\ km}\end{array}$