Arithmatical -Boats and Streams
DIRECTIONS : Problems based on Boats and Streams.
6. |
A boat covers a certain distance downstream in I hour, while it comes back in 1½ hours. If the speed of the stream be 3 kmph. what is the speed of the boat in still Water? |
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A. 12kmph |
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B. 13kmph |
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C. 15kmph |
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D. 16kmph |
Solution |
Let the speed of the boat in still water be x kmph. Then, |
Speed downsteram | = (x + 3) kmph. |
Speed upsteram | = (x - 3) kmph. |
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= (x+3)x1 |
= (x - 3)x3/2 kmph. |
= 2x+6 = 3x-9 |
x= 15 kmph. |
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7. |
A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr The man's speed against the current is |
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A. 8.5 km/hr |
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B. 9 km/hr |
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C. 10 km/hr |
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D. 12.5 km/hr |
Solution |
Man's rate in still water | = (15 - 2.5) km/hr |
= 12.5 km/hr. |
Man's rate against the current | = (12.5 - 2.5) km/hr |
= 10 km/hr. |
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8. |
A man can row upstream at 7 kmph and downstream at 10 kmph.Find man's rate in still water and the rate of current? |
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A. 1.2 km/hr |
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B. 1.5 km/hr |
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C. 1.6 km/hr |
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D. 1.8 km/hr |
Solution |
Rate in still water | = 1 / 2 (10 + 7) km/hr |
= 8.5 km/hr. |
Rate of current | = 1 / 2(10 - 7) km/hr |
= 1.5 km/hr. |
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9. |
A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water? |
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A. 40 minutes |
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B. 1 hour |
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C. 1 hour 15 min |
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D. 1 hour 30 min |
Solution |
Rate downstream | = (1 / 10 x 60)km/hr |
= 6 km / hr. |
Rate upstream | = 2 km/hr. |
Speed in still water | = 1 / 2(6 + 2)km/hr |
= 4 km. |
Required time | = (5 / 4) km/hr |
= 1x 1/4 km/hr |
= 1 hr 15 min. |
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