IPMAT Rohtak 2019 (QA) - If the speed of boat in still water on Saturday was 27 km/hr and the speed of boat in still water on Wednesday was 66 2/3\% more than that of Saturday and time taken to travel upstream on Wednesday is 16/13 times than time taken by it to travel downstream on Saturday, then find the speed of stream (in kmph) on Saturday? | PYQs + Solutions

IPMAT Rohtak 2019

Arithmetic

Time, Speed & Distance

Medium

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If the speed of boat in still water on Saturday was 27 km/hr and the speed of boat in still water on Wednesday was $66 \frac{2}{3}\%$ more than that of Saturday and time taken to travel upstream on Wednesday is $\frac{16}{13}$ times than time taken by it to travel downstream on Saturday, then find the speed of stream (in kmph) on Saturday?

Correct Option: 3

Let speed of boat Upstream be -

U

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Let speed of boat Downstream be -

D

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Let speed of boat in still water be -

B

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Let speed of stream be -

W

U = B - W

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D = B + W

Given on Saturday:

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B_{sat} = 27 \text{ kmph}

On Wednesday:

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B_{wed} = B_{sat} + 66\frac{2}{3}\% \times B_{sat}

B_{wed} = 27 + \frac{200}{3} \times \frac{27}{100} = 45 \text{ kmph}

Let time taken to travel downstream on Saturday be -

t

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Time taken to travel upstream on Wednesday

= \frac{16}{13}t

On Wednesday:

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W_{wed} = 6 \text{ kmph}

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U_{wed} = B_{wed} - W_{wed} = 45 - 6 = 39 \text{ kmph}

Distance travelled upstream on Wednesday

= 12\% \text{ of } 4800 = 576 \text{ km}

Time taken upstream on Wednesday

= \frac{576}{39} = \frac{192}{13} \text{ hours}

\frac{16}{13}t = \frac{192}{13}

t = 12 \text{ hours}

Time taken downstream on Saturday

= 12 \text{ hours}

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Distance covered downstream on Saturday

= 432 \text{ km}

Speed downstream on Saturday

= \frac{432}{12} = 36 \text{ kmph}

D_{sat} = B_{sat} + W_{sat}

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36 = 27 + W_{sat}

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W_{sat} = 9 \text{ kmph}

Therefore, speed of stream on Saturday is

9 \text{ kmph}