A) 2.4 km/hr.
B) 2 km/hr.
C) 3 km/hr.
D) 0.75 km/hr.
Correct Answer: B
Solution :
[b] Let upstream rate = x km/hr Downstream rate = y km/hr \[\therefore \] \[\frac{24}{x}+\frac{36}{y}=6\] ? (1) \[\frac{36}{x}+\frac{24}{y}=\frac{13}{2}\] ? (2) Add (1) and (2), we get \[60\left( \frac{1}{x}+\frac{1}{y} \right)=\frac{25}{2}\Rightarrow \frac{1}{x}+\frac{1}{y}=\frac{2}{24}\] ? (3) Subtract (1) from (2) \[12\left( \frac{1}{x}-\frac{1}{y} \right)=\frac{1}{2}\Rightarrow \frac{1}{x}-\frac{1}{y}=\frac{1}{24}\] ? (4) Add (3) and (4) \[\frac{2}{x}=\frac{6}{24}\Rightarrow x=8\] From (3) y = 12 \[\therefore \,\,\,Velocity\,\,of\,\,current=\frac{1}{2}(y-x)=\frac{1}{2}(12-8)=2km/hr\]
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