IPMAT Rohtak 2019 (QA) - The speed of boat in still water on Saturday was 21 km/hr, and that on Sunday was 28 4/7\% more than that on Saturday. If the time taken by boat to travel upstream on Saturday is 21/2 times the time taken to travel downstream on Sunday, then find the time taken by the boat to cover a distance of 125 km upstream on Saturday? | PYQs + Solutions

IPMAT Rohtak 2019

Arithmetic

Time, Speed & Distance

Medium

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The speed of boat in still water on Saturday was 21 km/hr, and that on Sunday was $28 \frac{4}{7}\%$ more than that on Saturday. If the time taken by boat to travel upstream on Saturday is $2\frac{1}{2}$ times the time taken to travel downstream on Sunday, then find the time taken by the boat to cover a distance of 125 km upstream on Saturday?

6 hrs 45 min

2 hrs 45 min

4 hrs 30 min

6 hrs 15 min

Correct Option: 4

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

B_{sat} = 21 \text{ kmph}

B_{sun} = 21 + 28\frac{4}{7}\% \text{ of } 21 = 21 + \frac{200}{700} \times 21 = 21 + 6 = 27 \text{ kmph}

W_{sun} = 3 \text{ kmph}

D_{sun} = B_{sun} + W_{sun} = 27 + 3 = 30 \text{ kmph}

Time taken to travel downstream on Sunday

= \frac{\text{Downstream distance travelled on Sunday}}{D_{sun}} = \frac{12}{30} = \frac{12 \times 24}{30} = 9.6 \text{ hrs}

Time taken to travel upstream on Saturday

= 2\frac{1}{2} \text{ times the Time taken to travel downstream on Sunday} = \frac{5}{2} \times 9.6 = 24 \text{ hrs}

Time taken to travel upstream on Saturday

= 24 \text{ hrs}

Distance covered upstream on Saturday

= 10\% \text{ of } 4800 = 480

Time taken to cover

125

km upstream on Saturday

=

?

24 \text{ hrs} \rightarrow 480 \text{ km}

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? \rightarrow 125 \text{ km}

= \frac{24 \times 125}{480} = 6.25 \text{ hrs}

So, time taken by the boat to cover a distance of

125

km upstream on Saturday

= 6 \text{ hours } 15 \text{ minutes}