Ram and Krishna moving towards each other met at some point and reach

Question

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

(A) √5 : 1
(B) 1 : 25
(C) 25 : 1
(D) 1 : √5
(E) None of these

GMATGuruNY · Accepted Answer

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} A

ashakank · Answer

R= t+10
K=t+50

Speed Ram = a
Speed Krishna =b

at =b(50)
bt=a(10)

t= root(500)=10root(5)

a/b = 50/t =5/root(5) = root(5)/1

sting8 · Answer

Handy result to remember   
 
When 2 bodies A and B are moving towards each other (say A moves towards end Q and B moves towards end P of a road PQ, where A started from P and B started from Q), such that
  After meeting each other, A takes x time units to reach end Q 
 After meeting each other, B takes y time units to reach end P

Then, the time taken by A and B to meet each other =  \sqrt{x*y}

For this question, time to meet =  \sqrt{50*10} = 10 \sqrt{5} min

P-------------R-------------Q

So, A takes  10 \sqrt{5}min  to reach R from P
And, B takes 50 min to reach P from R

As distance PR remains same
 \frac{A}{B} = \frac{50 }{ 10 \sqrt{5}} = \frac{\sqrt{5}}{1}

lakshya14 · Answer

If Time and speed ratios are flipped, then why ratio of speed is not 1:5?

sting8 · Answer

After meeting, ram will have to cover the distance that Krishna has already covered and vice versa.

Ratio of speed is inversely proportional to ratio of time, when distance covered is same.

Here, since the distances being covered   after  meeting are not same, we cannot use the inverse ratio of times directly.

You can refer to my solution above, there the inverse ratio of time can be used, because the same distance is being considered.

Posted from my mobile device

bumpbot · Answer

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Ram and Krishna moving towards each other met at some point and reach

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