If a man travels at \(\frac{1}{x}\) km/h on a journey and returns at \(\rm \frac{1}{x^2}\) km/h, then his average speed for the journey is:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 3)

Answer 1

Given:

A man travels at \(\frac{1}{x}\) km/h on a journey and returns at \(\rm \frac{1}{x^2}\) km/h

Concept used:

Average speed = \(\frac{2\times speed_1\times speed_2}{speed_1 + speed_2}\)

Calculation:

Average speed = \(\frac{2\times\frac{1}{x}\times\frac{1}{x^2}}{\frac{1}{x}+\frac{1}{x^2}}\)

⇒ \(\frac{\frac{2}{x^3}}{\frac{x + 1}{x^2}}\)

⇒ \(\rm \frac{2}{x+x^2}\)

∴ The average speed is \(\rm \frac{2}{x+x^2}\).