Subject: General Aptitude · Chapter: Time and Distance · Exam: 2007 · Marks: · Difficulty:
A person travels three equal distances at a speed of $x \mathrm{km} / \mathrm{hr}, y \mathrm{km} / \mathrm{hr}$ and $z \mathrm{km} / \mathrm{hr}$ respectively. What is the average speed for the whole journey?
(a)$\frac{x y z}{3(x y+y z+z x)}$
(b)$\frac{x y z}{(x y+y z+z x)}$
(c)$\frac{(x y+y z+z x)}{x y z}$
(d)$\frac{3 x y z}{(x y+y z+z x)}$
Answer
Answer (as printed): D
Explanation
Let each distance be equal to $d$. Then, Total distance travelled $=3 d$. $$\begin{aligned} \text { Total time taken } & =\left(\frac{d}{x}+\frac{d}{y}+\frac{d}{z}\right) \mathrm{hr}=\frac{d(x y+y z+z x)}{x y z} \mathrm{hr} . \\ \therefore \text { Average speed } & =\left[3 d \times \frac{x y z}{d(x y+y z+z x)}\right] \mathrm{km} / \mathrm{hr} \\ & =\frac{3 x y z}{(x y+y z+z x)} \mathrm{km} / \mathrm{hr} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.