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Question:

A motorboat takes the passengers from Rishikesh to Haridwar and back. Both the cities, Rishikesh and Haridwar are located on the banks of River Ganga. During Kumbh Mela, to earn more money, the owner of the motorboat decided to have more trips from Rishikesh to Haridwar and back, so he increased the speed of the motorboat in still water, by 50%. By increasing the speed, he was able to cut down the travel time from Rishikesh to Haridwar and back, by 60%. What is the ratio of the speed of motorboat in still water to that of the speed of river Ganga?

Explanation:

Let the speed of boat in still water be ‘b’ and speed of river be ‘r’ and the one-way distance between the two cities be ‘d’.

Time taken initially to go and come back = $\frac{d}{b + r}$ + $\frac{d}{b - r}$

When the speed of boat increases by 50%, time taken to go and come back = $\frac{d}{1.5 b + r}$ + $\frac{d}{1.5 b - r}$

New time taken is 40% of the initial time taken

⇒ $\frac{d}{1.5 b + r} + \frac{d}{1.5 b - r}$ = $\frac{2}{5} [\frac{d}{b + r} + \frac{d}{b - r}]$

⇒ $\frac{3 b}{2.25 b^{2} - r^{2}}$ = $\frac{2}{5} [\frac{2 b}{b^{2} - r^{2}}]$

⇒ 15b² – 15r²= 9b² – 4r²

⇒ 6b² = 11r²

⇒ $\frac{b}{r}$ = $\sqrt{\frac{11}{6}}$

Hence option (a).

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