A) 5 km/h
B) 8 km/h
C) 10 km/h
D) 15 km/h
Correct Answer: A
Solution :
| Let the speed of the stream be x km/h. |
| Speed downstream \[=(15+x)km/h\] |
| Speed upstream \[=(15-x)km/h\] |
| \[\frac{30}{(15+x)}+\frac{30}{(15-x)}=4\frac{30}{60}\] |
| \[\Rightarrow \] \[\frac{30}{(15+x)}+\frac{30}{(15-x)}=\frac{9}{2}\] |
| \[\Rightarrow \] \[\frac{1}{(15+x)}+\frac{1}{(15-x)}=\frac{9}{2\times 30}=\frac{3}{20}\] |
| \[\Rightarrow \] \[\frac{(15-x)+(15+x)}{(15+x)(15-x)}=\frac{3}{20}\] |
| \[\Rightarrow \] \[3\,\,(225-{{x}^{2}})=600\] |
| \[\Rightarrow \] \[3{{x}^{2}}=75\]\[\Rightarrow \]\[{{x}^{2}}=25\]\[\Rightarrow \]\[x=5\] |
| Speed of stream = 5 km/h |
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