A) 1.5 km/h
B) 1 km/h
C) 2 km/h
D) 2.5 km/h
Correct Answer: C
Solution :
| [c] If the speed of boat in still water be x km/h and speed of current by \[y\text{ }km/h.\] |
| Then, speed in downstream \[=(x+y)\] |
| Speed in upstream \[=(x-y)\] |
| According to the question, |
| \[\frac{12}{x-y}+\frac{18}{x+y}=3\] . (i) |
| \[\frac{36}{x-y}+\frac{24}{x+y}=\frac{13}{2}\] . (ii) |
| On multiplying Eq. (i) by 3 and subtracting Eq. (ii) from Eq. (i), |
| \[\frac{54}{x+y}-\frac{24}{x+y}=9-\frac{13}{2}\]\[\Rightarrow \]\[\frac{30}{x+y}=\frac{5}{2}\] |
| \[\Rightarrow \] \[x+y=12\] (iii) |
| On substituting the value \[(x+y)\] of from Eq. (iii), we get \[\frac{12}{x-y}+\frac{18}{12}=3\] |
| \[\Rightarrow \] \[\frac{12}{x-y}=3-\frac{3}{2}=\frac{3}{2}\] |
| \[\Rightarrow \] \[x-y=\frac{12\times 2}{3}=8\] . (iv) |
| Speed of current \[=\frac{1}{2}\](speed downstream |
| - Speed upstream) |
| \[=\frac{1}{2}(12-8)=2\,km/h\] |
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