In covering a distance of 150 km, Pranay takes 2 hours more than Aman. If Pranay doubles his speed, then he would take 3 hours less than Aman. Pranay's speed is:

The correct option is 15 km/hr.

Step-by-Step Explanation:

Step 1: Define the variables
Let the speed of Pranay be $x$ km/hr.
Let the speed of Aman be $y$ km/hr.
The total distance to cover is 150 km.

Step 2: Formulate the equations based on time
We know that $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$.

Time taken by Pranay to cover 150 km = $\frac{150}{x}$ hours.

Time taken by Aman to cover 150 km = $\frac{150}{y}$ hours.

According to the first condition, Pranay takes 2 hours more than Aman:

$\frac{150}{x}-\frac{150}{y}=2$    --- (Equation 1)

According to the second condition, if Pranay doubles his speed to $2x$ km/hr, he takes 3 hours less than Aman:

$\frac{150}{y}-\frac{150}{2x}=3$    --- (Equation 2)

Step 3: Solve the system of equations
Add Equation 1 and Equation 2 together to eliminate the term containing $y$:

$\left(\frac{150}{x}-\frac{150}{y}\right)+\left(\frac{150}{y}-\frac{150}{2x}\right)=2+3$

$\frac{150}{x}-\frac{150}{2x}=5$

Taking $\frac{150}{x}$ common:

$\frac{150}{x}\left(1-\frac{1}{2}\right)=5$

$\frac{150}{x}\left(\frac{1}{2}\right)=5$

$\frac{75}{x}=5$

$x=\frac{75}{5}$

$x=15$

Thus, Pranay's speed is 15 km/hr.