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The distance between two points is 36 km. A boat rows in still water at 6 kmph. It takes 8 hours less to cover this distance in downstream in comparison to that in upstream. The rate of stream is
|
A) 3 kmph |
|
B) 2 kmph |
|
C) 2.5 kmph |
|
D) 4 kmph |
Correct Answer:
| A) 3 kmph |
Description for Correct answer:
Speed of current = x kmph
\( \Large \therefore \) Rate downstream
= (6 + x) kmph
Rate upstream = (6 - x) kmph
\( \Large \therefore \frac{36}{6 - x} - \frac{36}{6 + x} = 8 \)
=> \( \Large 36(\frac{6 + x - 6 + x}{(6 - x)(6 + x)}) = 8 \)
=> \( \Large \frac{36 \times 2x}{(6 - x)(6 + x)} = 8 \)
=> \( \Large 9x = 36 - x^{2} \)
=> \( \Large x^{2} + 9x - 36 = 0 \)
=> \( \Large x^{2} + 12x - 3x - 36 = 0 \)
=> \( \Large x(x + 12) - 3(x + 12) = 0 \)
=> \( \Large (x - 3) (x + 12) = 0 \)
=> x = 3 kmph
Speed of current = x kmph
\( \Large \therefore \) Rate downstream
= (6 + x) kmph
Rate upstream = (6 - x) kmph
\( \Large \therefore \frac{36}{6 - x} - \frac{36}{6 + x} = 8 \)
=> \( \Large 36(\frac{6 + x - 6 + x}{(6 - x)(6 + x)}) = 8 \)
=> \( \Large \frac{36 \times 2x}{(6 - x)(6 + x)} = 8 \)
=> \( \Large 9x = 36 - x^{2} \)
=> \( \Large x^{2} + 9x - 36 = 0 \)
=> \( \Large x^{2} + 12x - 3x - 36 = 0 \)
=> \( \Large x(x + 12) - 3(x + 12) = 0 \)
=> \( \Large (x - 3) (x + 12) = 0 \)
=> x = 3 kmph
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