A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is

The correct option is 2.

Let us break down the problem step-by-step to understand how we arrive at this solution.

Suppose Ram starts from point A and Rahim starts from point B at the same time. Let them meet at some point C on the straight line between A and B.
Let the speed of Ram be $s_1$ and the speed of Rahim be $s_2$.
Since they start at the same time, let $t$ be the time they take to travel from their respective starting points to meet at point C.

During this time $t$:
Ram travels from A to C, covering a distance of:
$\text{Distance(AC)}=s_1\times t$
Rahim travels from B to C, covering a distance of:
$\text{Distance(BC)}=s_2\times t$

After crossing each other at point C:
Ram continues to run from C to B (distance BC) at his speed $s_1$ and reaches point B in 1 minute.
Therefore, we can write:
$\text{Distance(BC)}=s_1\times 1$
Substituting the value of Distance(BC) from the earlier equation:
$s_2\times t=s_1\times 1$
Solving for $t$, we get:
$t=\frac{s_1}{s_2}$
This is our first equation.

Similarly, after crossing at point C, Rahim continues to run from C to A (distance AC) at his speed $s_2$ and reaches point A in 4 minutes.
Therefore, we can write:
$\text{Distance(AC)}=s_2\times 4$
Substituting the value of Distance(AC) from the earlier equation:
$s_1\times t=s_2\times 4$
Solving for $t$, we get:
$t=\frac{4s_2}{s_1}$
This is our second equation.

Since the time taken to meet ($t$) is the same for both, we can equate the two expressions for $t$:
$\frac{s_1}{s_2}=\frac{4s_2}{s_1}$
Cross-multiplying the terms gives:
${\left(s_1\right)}^2=4{\left(s_2\right)}^2$
Taking the positive square root on both sides:
$s_1=2s_2$
Rearranging to find the ratio of Ram's speed to Rahim's speed:
$\frac{s_1}{s_2}=2$

Thus, the ratio of Ram's speed to Rahim's speed is 2.