A) 20 km/h
B) 30 km/h
C) 26 km/h
D) 48 km/h
E) None of these
Correct Answer: C
Solution :
Explanation Let the speed of the steamer in still water be x km/h. It is given that while going down stream the steamer takes 6 hours to cover the distance between two ports. \[\therefore \]. Speed of the steamer down-stream \[=\, \left( x + 2 \right) km/h.\] Distance covered in \[1 h = \left( x + 2 \right) km\] Distance covered in \[6 h = 6\left( x + 2 \right) km\] \[\therefore \] Distance between 2 ports \[= 6\left( x + 2 \right) km\]............... (i) It is given that while going up stream, the steamer takes 7 hours to cover the distance. Speed of the steamer up stream \[=\,\, \left( x - 2 \right) km/h\] Distance covered in \[1 h = \left( x - 2 \right) km\] Distance covered in \[7 h = 7 \left( x - 2 \right) km\] \[\therefore \] Distance covered in this case\[= 7 \left( x - 2 \right) km\]............ (ii) \[\therefore \] The distance between two ports is same \[\therefore \] From (i) and (ii) we get \[6\left( x+2 \right)=7\left( x\,-2 \right)\] \[6x+12=7x\,-14\] \[\Rightarrow \,\,\,\,6x\,-7x\,\,=\,\,-14\,\,-12\] [Transposing 7x to L.H.S. and 12 to R.H.S.] \[\Rightarrow \,\,\,-x=-26\] \[\Rightarrow \,\,\,x=26\] \[\therefore \] The speed of the streamer in still water \[= \,26 km/hr.\]
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