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Question

A motorboat covers a given distance in 6hour moving downstream on a river. It covers the same distance in10 hour moving upstream. The time it takes to cover the same distance in still water is


A

9 hour

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B

7.5 hour

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C

6.5 hour

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D

8 hour

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Solution

The correct option is B

7.5 hour


Explanation for the correct option:

Step 1. Assume the velocity of water and motorboat :

Let, the velocity of water =w

and the velocity of the motorboat in still water =s

The distance covered by a motorboat in moving downstream in 6hr is

=(s+w)×6 (distance = velocity x time)

The same distance covered by the motorboat in moving upstream in 10hr is

=(s-w)×10

Step 2. Apply the condition :

(s+w)×6=(s-w)×10

6s+6w=10s-10w

16w=4s

w=0.25s

So, distance =(s+w)×6

=(s+0.25s)×6

=7.5s

Step 3. Calculate the time :

The time is taken by the motorboat to cover the same distance in still water

Time=Distances

=7.5ss

=7.5 hour

Hence, the correct option is B.


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