Institution: AGRANI BANK LTD Exam: Agrani bank Ltd - Officer - 12.02.2010
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To determine the speed for the return trip, we first calculate the time taken for the initial 10-mile journey. The speed is 50 miles per hour, so the time \( t \) for this trip can be calculated using the formula:

\[
t = \frac{d}{s} = \frac{10 \text{ miles}}{50 \text{ miles per hour}} = 0.2 \text{ hours} = 12 \text{ minutes}.
\]

Since the total round trip time is 20 minutes, this means the return trip must take:

\[
20 \text{ minutes} - 12 \text{ minutes} = 8 \text{ minutes}.
\]

We convert 8 minutes into hours for the speed calculation:

\[
8 \text{ minutes} = \frac{8}{60} \text{ hours} = \frac{2}{15} \text{ hours}.
\]

Now, using the formula for speed \( s = \frac{d}{t} \) for the return trip (which is still 10 miles), we find the required speed:

\[
s = \frac{10 \text{ miles}}{\frac{2}{15} \text{ hours}} = 10 \times \frac{15}{2} = 75 \text{ miles per hour}.
\]

Thus, the required speed for the emergency vehicle on the return trip is indeed 75 mph, corresponding to option D.