Question

# A motorboat covers a given distance in $6$hour moving downstream on a river. It covers the same distance in$10$ 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 $7.5$ hourExplanation 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 $6$hr is$=\left(s+w\right)×6$ (distance = velocity x time) The same distance covered by the motorboat in moving upstream in $10$hr is$=\left(s-w\right)×10$Step 2. Apply the condition : $\left(s+w\right)×6=\left(s-w\right)×10$$⇒$ $6s+6w=10s-10w$$⇒$ $16w=4s$$⇒$ $w=0.25s$So, distance $=\left(s+w\right)×6$ $=\left(s+ 0.25s\right)×6$ $=7.5s$Step 3. Calculate the time : The time is taken by the motorboat to cover the same distance in still water $Time=\frac{Dis\mathrm{tan}ce}{s}$ $=\frac{7.5s}{s}$ $=7.5$ hourHence, the correct option is B.

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