A) 1 km/h
B) 2 km/h
C) 1.5 km/h
D) 2.5 km/h
Correct Answer: B
Solution :
Speed of boat in still water = x km/h Speed of current = y km/h \[\therefore \] \[\frac{24}{x-y}+\frac{36}{x+y}=6\] ?(i) and \[\frac{24}{x+y}+\frac{36}{x-y}=\frac{13}{2}\] ?(ii) By Eq. (i) \[\times \,\,2-\]Eq. (ii) \[\times \,\,3,\]we have \[\frac{48}{x-y}-\frac{108}{x-y}=12-\frac{39}{2}\] \[\Rightarrow \]\[\frac{60}{x-y}=\frac{15}{2}\] \[\Rightarrow \] \[x-y=8\] ...(iii) By Eq. (i) \[\times \,\,3-\]Eq. (ii) \[\times \,\,2,\]we have \[\frac{108}{x+y}-\frac{48}{x+y}=18-13\] \[\Rightarrow \]\[\frac{60}{x+y}=5\] \[\Rightarrow \]\[x+y=12\] ?(iv) On subtracting Eq. (iii) from Eq. (iv), we get \[x+y-x+y=12-8\] \[2y=4\] \[y=2\,\,\text{km/h}\]
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