Question

A man travels three-fifths of a distance AB at a speed 3a, and the remaining at a speed 2b. If he goes from B to A and returns at a speed 5c in the same time, then

• A. $\frac{1}{a} + \frac{1}{b} = \frac{1}{c}$
• B. $a + b = c$
• C. $\frac{1}{a} + \frac{1}{b} = \frac{2}{c}$
• D. None of these

Hint:

Time = distance/speed; equate when total times are equal.

Answer 1

The Correct Option is A

Forward time = $\frac{3d/5}{3a} + \frac{2d/5}{2b} = \frac{d}{5a} + \frac{d}{5b} = \frac{d}{5}(\frac{1}{a} + \frac{1}{b})$.
Return time = $\frac{d}{5c}$. Equal times → $\frac{1}{a} + \frac{1}{b} = \frac{1}{c}$.