The speeds of two cars A and B are in the ratio 3 : 2. Car A travels for 4 hours, while Car B travels for 5 hours. If the difference between the distances covered by the two cars is 20 km, then find the speed of Car B (in km/hr).

The correct answer is 20.

Step-by-step Explanation:

Step 1: Define the speeds of the cars using a variable.
The speeds of Car A and Car B are given in the ratio 3 : 2.
Let the speed of Car A be $3x$ km/hr and the speed of Car B be $2x$ km/hr, where $x$ is a constant multiplier.

Step 2: Calculate the distance traveled by each car.
We know the formula for distance is:

$\text{Distance}=\text{Speed}\×\text{Time}$

${\text{Distance}}_{\mathrm{A}}=3x\×4=12x\text{km}$

${\text{Distance}}_{\mathrm{B}}=2x\×5=10x\text{km}$

Step 3: Set up the equation using the given difference in distances.
The difference between the distances covered by Car A and Car B is 20 km.

${\text{Distance}}_{\mathrm{A}}-{\text{Distance}}_{\mathrm{B}}=20$

$12x-10x=20$

$2x=20$

$x=10$

Step 4: Find the speed of Car B.
The speed of Car B is $2x$ km/hr.
Substituting $x=10$:

$\text{Speed of Car B}=2\×10=20\text{km/hr}$