IPMAT Rohtak 2019 (QA) - If the time taken by boat to travel upstream on Monday is 27 1/5 hrs more than the time taken by it to travel downstream on the same day, then find the speed of boat in still water on Monday? (speed of boat in still water is the same in upstream as in downstream) | PYQs + Solutions

IPMAT Rohtak 2019

Arithmetic

Time, Speed & Distance

Medium

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If the time taken by boat to travel upstream on Monday is $27 \frac{1}{5}$ hrs more than the time taken by it to travel downstream on the same day, then find the speed of boat in still water on Monday? (speed of boat in still water is the same in upstream as in downstream)

25 kmph

18 kmph

20 kmph

15 kmph

Correct Option: 1

Let speed of the boat Upstream be -

U

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Speed of the boat Downstream be -

D

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Speed of boat in still water be -

B

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Speed of the stream be -

W

U = B - W

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D = B + W

On Monday distance covered Upstream

= 16\% \text{ of } 4800 = 768 \text{ km}

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Distance covered Downstream

= 14\% \text{ of } 2400 = 336 \text{ km}

Let time taken to cover downstream be -

t \text{ hrs}

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Then, time taken to cover upstream will be -

t + 27.2 \text{ hrs}

On Monday, Speed of still water(stream)

= W = 5 \text{ kmph}

U = B - 5

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D = B + 5

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D-U = B + 5 - (B - 5) = 10 \text{ kmph}

Also,

D = \frac{336}{t}

Also,

U = \frac{768}{t+27.2}

D - U = 10 \text{ kmph}

\frac{336}{t} - \frac{768}{t+27.2} = 10

10t + 704t - 9139.2 = 0

t = 11.2 \text{ hours}

So,

D = \frac{336}{11.2} = 30 \text{ kmph}

Also,

D = B + 5

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B + 5 = 30

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B = 25 \text{ kmph}

Therefore, the speed of boat in still water on Monday is -

25 \text{ kmph}