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A boat covers a distance of 2.75 km upstream in 11 minutes. The ratio between speed of current and that of boat downstream is 1 : 7 respectively. The boat covers distance between A and B downstream in 52 minutes. What is the distance between point A and point B ?
|
A) 19.2 km. |
|
B) 17.2 Km. |
|
C) 18.2 km. |
|
D) 16.5 km. |
Correct Answer:
| C) 18.2 km. |
Description for Correct answer:
Speed of boat in still water = x kmph
Speed of current = y kmph
\( \Large \therefore \) Rate downstream
= (x + y) kmph
Rate upstream = (x - y) kmph
\( \Large \therefore \frac{y}{x + y} = \frac{1}{7} \)
=> 7y = x + y
=> x = 6y
Again, \( \Large \frac{2.75}{x - y} = \frac{11}{60} \)
=> \( \Large 11 (x - y) = 2.75 \times 60 = 165 \)
=> \( \Large x - y = \frac{165}{11} = 15 \)
=> 6y - y = 15
=> 5y = 15
=> y = 3 kmph
\( \Large \therefore x = 6 \times 3 = 18 kmph \)
\( \Large \therefore \) x + y = Rate downstream
= 18 + 3 = 21 kmph
Distance between points A and B
= \( \Large \ Rate \ downstream \times \ Time \)
= \( \Large \frac{21 \times 52}{60} = 18.2 \ km \)
Speed of boat in still water = x kmph
Speed of current = y kmph
\( \Large \therefore \) Rate downstream
= (x + y) kmph
Rate upstream = (x - y) kmph
\( \Large \therefore \frac{y}{x + y} = \frac{1}{7} \)
=> 7y = x + y
=> x = 6y
Again, \( \Large \frac{2.75}{x - y} = \frac{11}{60} \)
=> \( \Large 11 (x - y) = 2.75 \times 60 = 165 \)
=> \( \Large x - y = \frac{165}{11} = 15 \)
=> 6y - y = 15
=> 5y = 15
=> y = 3 kmph
\( \Large \therefore x = 6 \times 3 = 18 kmph \)
\( \Large \therefore \) x + y = Rate downstream
= 18 + 3 = 21 kmph
Distance between points A and B
= \( \Large \ Rate \ downstream \times \ Time \)
= \( \Large \frac{21 \times 52}{60} = 18.2 \ km \)
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