Arithmetic

Time, Speed & Distance

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Figure for IPMAT Rohtak 2019 QA question 4 (Arithmetic)

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 - $U$

Speed of the boat Downstream be - $D$

Speed of boat in still water be - $B$

Speed of the stream be - $W$

$U = B - W$

$D = B + W$

$B_{sat} = 21 \text{ kmph}$

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

$W_{sun} = 3 \text{ kmph}$

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

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 $=$ $?$

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

$? \rightarrow 125 \text{ km}$

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

So, time taken by the boat to cover a distance of $125$ km upstream on Saturday $= 6 \text{ hours } 15 \text{ minutes}$

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IPMAT Rohtak 2019

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