Question

If a scooterist drives at the rate of $25\text{km/h}$ he reaches his destination $7\text{min}$ late and if he drives at the rate of $30\text{km/h}$ he reaches his destination $5\text{min}$ earlier. How far is his destination?

• A. $20\text{km}$
• B. $25\text{km}$
• C. $30\text{km}$
• D. $32\text{km}$

Answer 1

The correct option is C $30\text{km}$

Let the distance be $x\text{km}$ far.
From the given information we can conclude that the difference between the time taken at the given two speeds is $12\text{min}.$

Now, by using the relation between distance, time, and speed,

$\begin{array}{cc}\frac{x}{25}-\frac{x}{30}& =\frac{12}{60}\\ \frac{6x-5x}{150}& =\frac{1}{5}\\ x& =\frac{150}{5}\\ & =30\text{km}\end{array}$

Hence, the desired destination is $30\text{km}$ far.