Question

Travelling at ${\frac{4}{5}}^{th}$ of his usual speed a man reaches his destination $15$ minutes late. If he travels the same distance $20\%$ faster than his usual speed, he would reach his destination_____.

• A. $15$ min early
• B. $20$ min early
• C. $5$ min early
• D. $10$ min early

Answer 1

The correct option is D $10$ min early

Let the Time taken on usual speed $v$ be $T$

Such that, $\frac{D}{v}=T$

Now, $\frac{D}{\frac{4}{5}v}=T+15\Rightarrow \frac{5}{4}\ast \frac{D}{v}=T+15\Rightarrow \frac{5}{4}T=T+15\Rightarrow \frac{T}{4}=15\Rightarrow T=60$

Now, as speed is increased by 20% it become $\frac{120}{100}v=\frac{6}{5}v$

So, Time = $\frac{D}{\frac{6}{5}v}=\frac{5}{6}T=\frac{5}{6}\ast 60=50$

Hence, it will reach 10 minutes early