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Let’s assume the speed of the boat in still water and the speed of the stream are ‘B’ and ‘C’ respectively.
A boat can cover ‘y’ km distance downstream in (t+2.5) hours.
(B+C) = y/(t+2.5)
y/(B+C) = (t+2.5) Eq.(i)
The same boat can cover ‘0.25y’ km distance upstream in ‘t’ hours.
(B-C) = 0.25y/t
0.25y/(B-C) = t
y/[4(B-C)] = t
y/(B-C) = 4t Eq.(ii)
If the total time taken by the boat to cover ‘y’ km distance downstream and the same distance upstream is 65 hours.
(y/(B+C))+(y/(B-C)) = 65
Put Eq.(i) and Eq.(ii) in the above equation.
(t+2.5)+4t = 65
5t+2.5 = 65
5t = 65-2.5
5t = 62.5
t = 12.5 Eq.(iii)
The time taken by the boat to cover 728 km in still water is (2t+3) hours.
728/B = (2t+3)
Put the value of ‘t’ from Eq.(iii) in the above equation.
728/B = (2x12.5+3)
728/B = (25+3)
728/B = 28
728/28 = B
B = 26 Eq.(iv)
Put the value of ‘B’ and ‘t’ in Eq.(i) and Eq.(ii).
y/(26+C) = (12.5+2.5)
y = 15(26+C) Eq.(v)
y/(26-C) = 4x12.5
y/(26-C) = 50
y = 50(26-C) Eq.(vi)
Equating Eq.(v) Eq.(vi).
15(26+C) = 50(26-C)
3(26+C) = 10(26-C)
78+3C = 260-10C
13C = 260-78
13C = 182
C = 14
So the speed of the stream = 14 km/h
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