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Boat A travels upstream from point X to point Y in 2 hours more than the time taken by Boat B to travel downstream from point Y to point Z. The distance between X and Y is 40 km and that distance between Y and Z is 24 km. The speed of Boat B in still water is 10 km/h and the speed of Boat A in still water is equal to the speed of Boat B downstream. What is the speed of Boat A in still water? (Consider the speed of the current to be the same).
A) 20 km/h
B) 10 km/h
C) 12 km/h
D) 14 km/h
Correct answer:
C) 12 km/h
Description for Correct answer:
Speed of current = x kmph
Rate downstream of boat B = (10 + x) kmph
Speed of boat A in still water = (10 + x)kmph
\( \Large \therefore \) Rate upstream
= 10 kmph
According to the question,
\( \Large \frac{40}{10} - \frac{24}{10 + x} = 2 \)
=> \( \Large \frac{24}{10 + x} = 4 - 2 = 2 \)
=> 10 + x = 12
=> x = 2 kmph
\( \Large \therefore \) Speed of boat A in still water
= 10 + 2 = 12 kmph
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