Correct Answer: The distance between Mr. Zaman’s office from his home is 6km.

Explanation:

Let, the distance between Mr. Zarnan’s office from his home is x km.

We know, 60 minutes = 1 hour

Here, 7 min = $\frac{7}{60}$

And, 5 min = $\frac{5}{60}$

We know, speed = $\frac{Distance}{Time}$

Time = $\frac{Distance}{speed}$

At 5 miles per hour, we have real/actual/required time from office to home = $\frac{x}{5}$-$\frac{7}{60}$hour

And, At 6 miles per hour, we have real/actual/required time from office to home = $\frac{x}{6}$-$\frac{5}{60}$hour

According to the question

$\frac{x}{5}-\frac{7}{60} = \frac{x}{6}+\frac{x5}{60}$

=> $\frac{x}{5}-\frac{7}{6}=\frac{5}{60}+\frac{7}{60}$

=> $\frac{6x-5x}{30}=\frac{ 5+7}{60}$

=> $\frac{x}{30}$=$\frac{12}{60}$

=> x =$\frac{12}{60}$x30

x=6