Alisha has agreed to send Khushi a 20- megabyte file. They both have a broadband internet connection. Alisha has to upload her file to a server and then Khushi needs to download it from the same server. The broadband data transfer rates (speeds) are 1 megabit per second to upload a file and 8 megabits per second to download a file. If P and Q represent the time taken in seconds to upload and download Alisha’s file respectively then (P, Q) =?

Correct option is D

Let's break down the problem:
1. File Size Conversion:
o The file size is given in megabytes (MB), but the transfer rates are in megabits per second (Mbps).
o 1 byte = 8 bits, so:
20 MB = 20 × 8 = 160 megabits (Mb).
2. Time to Upload (P):
o Alisha's upload speed is 1 megabit per second.
o To find the time taken to upload, use the formula:
​$$\text{Time} = \frac{\text{File Size}}{\text{Speed}}$$​​
o Therefore:
​$$P = \frac{160 \, \text{megabits}}{1 \, \text{Mbps}} = 160 \, \text{seconds}$$​​
3. Time to Download (Q):
o Khushi's download speed is 8 megabits per second.
o Using the same formula for time:
​$$Q = \frac{160 \, \text{megabits}}{8 \, \text{Mbps}} = 20 \, \text{seconds}$$​​
Thus, the time taken to upload the file is 160 seconds, and the time taken to download the file is 20 seconds.
Information Booster:
• File Size Conversion: Since internet speeds are typically measured in megabits, we need to convert the file size from megabytes to megabits. This is important for accurately calculating the time taken for upload and download.
• Upload and Download Time Formula: The time to transfer a file can be calculated by dividing the file size (in megabits) by the transfer speed (in megabits per second).