Hope the serious CAT aspirants did give the problem their best shot. It should not be demoralising if you could not crack the problem. It is a very difficult one to begin with.
I can post the solution right away. But then no learning is going to happen. It is like giving a person a fish rather than help him teach fishing.
So, go through the following two clues. As I said the problem is a classic one to learn quite a lot of fundas...the two clues refer to two different fundas to learn.
Clue 1. Consider the same problem in a modified way. Lets say the guy travels from A to B (first downhill, then on plains and then uphill) and covers the distance AB in 4 hours. Say on the return journey also he takes 4 hours itself. The speed remains as 72 kmph downhill, 63 kmph on the plains and 56 kmph uphill.
Now what does 4 hours both way suggest. This should be easy.
Secondly, consider the data: "a person travels equal distances at speeds of 72 kmph and at 56 kmph". What can you infer from this data, how can you process it, what sort of standard question can be asked on just this simple data?
Clue 2: I travel a certain distance first at 72 kmph and then the same distance at 56 kmph. The difference in the time taken in the two cases is 40 minutes. Can you find the distance?
If you find the questions asked in both the above clues very easy, you are comforatble with the basic theory. If you yet could not solve the problem, the hurdle lies in applying these basic fundas (there is very little beyond the answers to questions asked in the clues, which considerred in isolation should be very easy).
This could simply be because of not enough attempt at surpassing your limits. Hence it is very important to struggle and learn the solution yourself. This land you in an upward spiral in cracking unseen problems. Do not have a affinity to check the solution untill you stay with the problem for atleast 1 day.
Another use of the above post could be to capture in your mindmap, standard questions or regular situations observed in problems. E.g. the question asked in second part of clue 1 is a straight forward problem of average speed. Lo! one more clue. If you missed this aspect, you are not focussing on the relevance of simple fundas taught. You are just looking at fundas taught as just one individual problem. Analysis the situation and data given in any standard problem till it is picture perfect in your mind.
Hope the above has helped you identify the hurdle you are facing and now get going and attempt a minimum of five problems from your regular material, right now, to correct your approach.
Chandra
4 comments:
Hi Chandra,
Juss check this.
In the second go,the person takes 40 min more => path to hill A is more lengthier than hill B
ie it is = 56 x 2/3 km more
=37.33 km
now the remaining part of hill A and hill B are equal,so going by your clue the avg.speed comes out to be 63
and total time taken is 4 hours
so this distance (inclusive of plains) will be = 63x4 = 252 km
so total distance must be
252 + 37.33 = 289.33 km
Where am i going wrong?
Hi Milind,
Good attempt. Path to hill A will not be just 56 x 2/3 km more. The extra path will be travelled @ 72 kmph downhill and @ 56 kmph uphill and the difference in the time taken 40 mins is th difference between these two times i.e. d/56 - d/72 = 2/3
Secondly, the time travelled @ average speed of 63 kmph is not entire 4 hours. SOme part of the 4 hours is used to travel the extra length of path to hill A. Time taken for this extra path is d/72. The rest of time is travelled at 63 kmph.
Does it help?
Chandra
Hi chandra
I got it.Dint consider the fact that 4 hrs should also include the time taken to travell the extra distance downhill.
Thanks!!
Just 1 query.had the speed on the pains not been 63 and since we dont know the length of the plains would be still able to find the average speed?
Hi Milind,
You are right, if the speed on the plains is not 63, we would not be able to find the distance uniquely. There would be infinite solutions. At one extreme, hilltop A to plian would be 168 kms and the rest 105 could all be plains i.e. no hill top B. At other extreme, there could be no plain and downhill from A would be 168 + 52.5 and uphill to B could be 52.5 km. Any solution between these two extremes could be possible.
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