The question is from the topic relative Speed. This is relatively a straightforward question and only tests the basic concepts. Time Speed and Distance is a favorite in CAT Exam and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam
Question 25: Two persons A and B start moving from point P towards Q which are 1400 Km apart. Speed of A is 50 Km/hr and that of B is 20 Km/hr. How far is A from Q when he meets B for the 22nd time?
Let's consider the Distance between P and Q, which is 1400km as one lap.
The Speeds of A and B are in the ratio 5 : 2. That means by the time A coimpletes 5 laps, B completes just 2 laps.
Both of them start moving from P, so after 5 laps(odd number of laps) A will be at Q, and B will be at P(even number of laps).
Seeing it from the perspective of A, he would have met P once evevy lap that he has made except the first lap since they are moving in the same dirction in the first lap.
So A and B would have met 5-1=4 times.
Let's consider another round of 5 laps. A runs 5 more laps and B runs 2 more laps
This time A starts from Q and after 5 laps reaches P, while in the same time B starts from P and ends at P.
This time they would have met exactly 5 times
Consolidating everything, we can say that A runs 10 rounds and B runs 4 rounds in the same time, reaching their original positions, meeting each other exactly 9 times
So cyclicity kicks in here....
22 can be written as 9 + 9 + 4.
After every 9 meets, A and B reach their original positions, that is both of them are at P. So, after 18 meets they both remain at P, For 4 more meets A must take 5 laps and B 2 laps, A being at Q and B at P at the end.
So at the end of this, A is at Q and B is at P.
That means the 22nd meet happened somewhere between and they travelled distances in the ratio of their speeds to reach P and Q
So distance between 22nd meet and Q is the distance travelled by A to reach Q ater the 22nd meet which is 5/7 * 1400 = 1000 km.
The question is " How far is A from Q when he meets B for the 22nd time? "
Choice A is the correct answer.
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