Question

Moving at 50 kmph, a person reaches his office 10 min late. Next day, he increases his speed and moves at 60 kmph and reaches his office 5 min early. What is the distance from his home to his office?

• A. 75 km
• B. 70 km
• C. 80 km
• D. 77 km

Answer 1

The correct option is A 75 km

We can observe that difference in timings on both days is $15$ min (and not $5$ min, as one day he is late and on the other day he is early)

Let the required distance $=D$ km.

As time taken at the speed of $50kmph$ is more than time taken at $60kmph$, so equation can be formed as $\frac{D}{50}-\frac{D}{60}=\frac{15}{60}$.

Solving this equation,$\frac{D}{50}-\frac{D}{60}=\frac{15}{60}$

$\Rightarrow \frac{60D-50D}{50\times 60}=\frac{15}{60}$

$\Rightarrow \frac{10D}{50}=15$

$\Rightarrow \frac{D}{5}=15$

$\Rightarrow D=15\times 5=75$

$\therefore$Distance from his home to his office is $75km$