Bunuel
Ram and Krishna moving towards each other met at some point and reached the opposite ends at their destinations 10 minutes and 50 minutes respectively
after the time of meeting. What is the ratio of their speeds?
(A) √5 : 1
(B) 1 : 25
(C) 25 : 1
(D) 1 : √5
(E) None of these
When two elements travel at different speeds, their TIME RATIO to travel the same distance will always be the same.
If R takes 1/2 as long as K to travel 10 miles, then R will take 1/2 as long as K to travel 1000 miles.
If R takes 3 times as long as K to travel 500 miles, then R will take three times as long as K to travel 2 miles.
Let M = the meeting point
Let t = the time for R and K each to travel to M
R:
----- t -----> M
----> 10 ----->K:
<---- 50 ----M
<------ t -------Since R takes t minutes to travel the blue portion, while K takes 50 minutes, the time ratio for R and K to travel the blue portion \(= \frac{t}{50}\)
Since R takes 10 minutes to travel the red portion, while K takes t minutes, the time ratio for R and K to travel the red portion \(= \frac{10}{t}\)
Since the time ratio in each case must be the same, we get:
\(\frac{t}{50} = \frac{10}{t}\)
\(t^2 = 500\)
\(t = 10\sqrt{5}\)
Time and rate have a RECIPROCAL relationship.
Since the time ratio for the red portion \(= \frac{10}{10\sqrt{5}} = \frac{1}{\sqrt{5}}\), the rate ratio \(= \frac{\sqrt{5}}{1}\)