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:

Answer: Option A

Solution

Answer: Option A

Solution:

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

Alternate

10% of journey's = 40 km
Then, total journey = 400 kms
$$\begin{array}{rl}& \text{And,}\text{Average speed}\\ & =\frac{\text{Total distance }}{\text{Total time}}\\ & 30\%\text{ of journey}\\ & =400\times \frac{30}{100}\\ & =120\text{ km}\\ & \\ & 60\%\text{ of journey}\\ & =400\times \frac{60}{100}\\ & =240\text{ km}\\ & \\ & 10\%\text{ of journey}\\ & =400\times \frac{10}{100}\\ & =40\text{ km}\\ & \text{Average speed}\\ & =\frac{400}{\frac{120}{20}+\frac{240}{40}+\frac{40}{10}}\\ & =\frac{400}{6+6+4}\\ & =\frac{400}{16}\\ & \therefore \text{Average speed}=25\text{ km/hr}\end{array}$$