Solve the quantitative aptitude problem below.
A drone's speed in calm air is 15 kmph, and the wind speed is 3 kmph. While traveling in the direction of the wind, the drone covers 108 km. Under these conditions, calculate the distance in km that the drone can cover in the same amount of time when traveling against the wind.

The correct answer is 72.

To find the distance covered by the drone when traveling against the wind, let us analyze the problem step-by-step.

Step 1: Calculate the effective speed in the direction of the wind (downstream).
When the drone travels in the direction of the wind, the wind assists the drone. Therefore, the effective speed is the sum of the drone's speed in calm air and the wind speed.

$\text{Downstream Speed (}{v}_{\text{down}}\text{)}=\text{Speed in calm air}+\text{Wind speed}$

$v_{\text{down}}=15\text{km/h}+3\text{km/h}=18\text{km/h}$

Step 2: Calculate the time taken to travel 108 km in the direction of the wind.
Using the formula $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$:

$t=\frac{108\text{km}}{18\text{km/h}}$

$t=6\text{hours}$

Step 3: Calculate the effective speed against the wind (upstream).
When traveling against the wind, the wind resists the movement of the drone. Therefore, the effective speed is the difference between the drone's speed in calm air and the wind speed.

$\text{Upstream Speed (}{v}_{\text{up}}\text{)}=\text{Speed in calm air}-\text{Wind speed}$

$v_{\text{up}}=15\text{km/h}-3\text{km/h}=12\text{km/h}$

Step 4: Calculate the distance covered against the wind in the same amount of time.
Using the formula $\text{Distance}=\text{Speed}\times \text{Time}$ for the time $t=6\text{hours}$:

$\text{Distance}=12\text{km/h}\times 6\text{hours}=72\text{km}$

Thus, the drone can cover a distance of 72 km when traveling against the wind in the same amount of time.