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Question

A boat goes 24 km upstream and 28 km down stream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is

A
10 km/hr
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B
4 km/hr
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C
14 km/hr
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D
6 km/hr
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Solution

The correct option is D 10 km/hr
Let speed of boat in still water be a km/hr.
Let rate of the current be b km/hr.
Speed of the boat upstream =(ab) km/hr.
24ab+28a+b=6 ...(i)
and 30ab+21a+b=132 ..(ii)
From (i) and (ii), we have
1ab=16 and 1a+b=114
ab=6 and a+b=14
a=10 km/hr.

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