| A boat covers \[25\,\,km\] upstream and \[24\,\,km\] downstream in \[16\,\,h\] while it covers \[20\,\,km\] upstream and 30 km downstream in \[15\frac{1}{2}h.\] The speed of current is |
A) \[\frac{1}{2}km/h\]
B) \[\frac{3}{4}km/h\]
C) \[\frac{1}{8}km/h\]
D) \[\frac{2}{3}km/h\]
Correct Answer: B
Solution :
| Let the upstream speed \[=x\,\,km/h.\] |
| Downstream speed \[=y\,\,km/h.\] |
| \[\frac{25}{x}+\frac{24}{y}=16\] (i) |
| \[\frac{20}{x}+\frac{30}{y}=\frac{31}{2}\] (ii) |
| Multiplying Eq. (i) by 4 and Eq. (ii) by 5 and subtracting, we get |
| \[\frac{54}{y}=\frac{27}{2}\]\[\Rightarrow \]\[y=\frac{54\times 2}{27}=4\] |
| Putting \[y=4\] in Eq. (i), we get \[x=2.5\] |
| Upstream speed \[=4\,\,km/h\]and downstream speed \[=2.5\,\,km/h\] |
| Speed of current \[=\frac{1}{2}(4-2.5)=\frac{3}{4}km/h\] |
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