The speeds of two cars A and B are in the ratio 25 : 24. If the difference in their speeds is 12 km/h, then find the speed of car A (in km/hr).

The correct answer is 300.

Let's solve the problem step-by-step to find the speed of car A.

Step 1: Understand the given ratio and setup variables
We are given that the ratio of the speeds of car A and car B is 25 : 24.
Let the speed of car A be $S_A$ and the speed of car B be $S_B$.
We can express their speeds in terms of a common constant ratio multiplier, $x$:

$S_A=25x$

$S_B=24x$

Step 2: Use the given difference in speeds
The difference between the speeds of car A and car B is given as 12 km/h.
Setting up the equation for the difference:

$S_A-S_B=12$

Substitute the expressions in terms of $x$:

$25x-24x=12$

$x=12$

Step 3: Calculate the speed of car A
Now, substitute the value of $x$ back into the expression for the speed of car A:

$S_A=25\times 12$

$S_A=300\text{km/h}$

Therefore, the speed of car A is 300 km/h.