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