A man travels equal distances of his journey at 40, 30 and 15 km/h. respectively. Find his average speed for whole journey.

A. 24

B. 25

C. 27

D. 28

Show Answer

Answer-A
Solution-

Solution(By Apex Team)


$\begin{array}{l}\text{Required average speed,}\\ =\Large\frac{(3 \times 40 \times 30 \times 15)}{(40 \times 30)+(40 \times 15)+(30 \times 15)} \\ =24 \mathrm{~km} / \mathrm{hr} \end{array}$

Alternately:

$\begin{array}{l}\text{Time taken to traveled}\\ =\Large\frac{1}{3}\end{array}$ distance of journey with speed 40 kmph, $\begin{array}{l}=\Large\frac{\frac{1}{3}}{40}=\frac{1}{120}\end{array}$ $\begin{array}{l}\text{Time taken to traveled}\\ =\Large\frac{1}{3}\end{array}$ distance of journey with speed 30 kmph, $\begin{array}{l}=\Large\frac{\frac{1}{3}}{30}=\frac{1}{90}\end{array}$ $\begin{array}{l}\text{Time taken to traveled}\\ =\Large\frac{1}{3}\end{array}$ distance of journey with speed 15 kmph, $\begin{array}{l}=\Large\frac{\frac{1}{3}}{15}=\frac{1}{45}\\ \text{ Total time taken }\\ =\Large\frac{1}{120}+\frac{1}{90}+\frac{1}{45}\\ =\Large\frac{45}{1080}\\ \text{Average speed}\\ =\left(\Large\frac{\text{Total distance travelled}}{\text{Total time taken}}\right)\\ =\Large\frac{1}{\frac{45}{1080}}\\ =24\mathrm{kmph}\end{array}$