Question

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

• A. \(2\)
• B. \(\sqrt2\)
• C. \(2\sqrt2\)
• D. \(\frac{1}{2}\)

Answer 1

The Correct Option is A

Required ratio of speeds = Square root of inverse ratio of times taken after crossing each other. 

= \(\sqrt4:\sqrt1\; i.e., 2:1\)

So, the correct answer is (A): \(2\)

Answer 2

Let Ram's speed be \(v(r)\) and Rahim's speed be \(v(h)\).
They will meet after a duration of \(t\) from the start.
Consequently, Ram will traverse a distance of \(v(r)(t)\) during this time, and Rahim will cover \(v(h)(t)\) respectively.
After meeting Ram reaches his destination in 1 min this means Ram covered \(v(h)t\) in 1 minute.
\(v(r)(1)= v(h)(t)\)     \(..……. (1)\)
Similarly, Rahim reaches his destination in 4 min this means Rahim covered v(r)t in 4 minutes.
\(v(h)(4)= v(r)(t) \)    \(……… (2)\)
On dividing eq \((1)\) and eq \((2)\),
\(\frac {v(r)}{4v(h)}=\frac {v(h)}{v(r)}\)

\([\frac {v(r)}{v(h)}]^2=4\)

\(\frac {v(r)}{v(h)}=\sqrt 4\)

\(\frac {v(r)}{v(h)}=2\)

So, the correct option is (A): \(2\)