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boat and river problem help needed
by rudrendra Kashyap - Tuesday, 26 August 2014, 06:35 PM
  Two boats start towards each other, from the two points exactly opposite of each other on the opposite banks of a river, simultaneously. They meet at a distance of 410 m from one of the banks and continue sailing further till they reach the opposite banks. They take rest for 1 hr each and start off the return journey taking the same route. Now they meet at a distance of 230 m from the other bank. Find the distance between the two banks. (Assume that river water is still.)
a. 750 m
b. 840 m
c. 1100 m
d. 1000 m
Re: boat and river problem help needed
by TG Team - Thursday, 28 August 2014, 11:38 AM
  Hi Rudrendra smile

The distance between the two banks is = 3(410) - 230 = 1000m. (option d)

Just observe that the moment the two boats meet for the first time, sum of distance travelled by the two boats is 'd' {if I assume the distance between two banks to be 'd'}.

Now next time when they meet, sum of the distance travelled by the two boats together becomes '3d' as both boats have reached to the opposite ends (i.e. travelled a distance of 'd' individually) and then turned back to meet at a point.

Clearly the ratio of time taken to meet for the first time and that to meet for second time is in the ratio of distances travelled i.e. 1 : 3. Also the distances travelled by any individual boat is also in the same ratio 1 : 3 as they also have travelled the distances for same time.

So the boat which had travelled 410m till first meeting, has travelled (d + 230)m for the second meeting. And that's how we get the above value for 'd'.

Hope it is clear. smile

Kamal Lohia