Question

Walking at three-fourth of his usual speed a man covers a certain distance in two hours more than the time he takes to cover the distance at his usual speed. The time taken by him to cover the distance with his usual speed is ___________.

• A. $4.5$ hours
• B. $5.5$ hours
• C. $6$ hours
• D. $5$ hours

Answer 1

The correct option is C $6$ hours

Let the distannce and usual speed be $x$ and $y$ respectively.

According to the question,

$\frac{x}{\left(\frac{3}{4}y\right)}-\frac{x}{y}=2$

$\frac{4}{3}\left(\frac{x}{y}\right)-\frac{x}{y}=2$

$\frac{x}{y}\times (\frac{4}{3}-1)$ = 2$

$\frac{x}{y}\times \frac{1}{3}=2$

$\frac{x}{y}=3\times 2=6$

Hence, time taken to cover the distance with usual speed = 6 h