A) 5 km/h
B) 4 km/h
C) 3 km/h
D) 2 km/h
Correct Answer: A
Solution :
Let speed of boat, \[{{S}_{1}}=11\,\text{km/h}\] and speed of stream be \[{{S}_{2}}\] In upstream, \[11-{{S}_{2}}=\frac{12}{{{t}_{1}}}\] \[\Rightarrow \] \[{{t}_{1}}=\frac{12}{11-{{S}_{2}}}\] and in downstream, \[11+{{S}_{2}}=\frac{12}{{{t}_{2}}}\] \[\Rightarrow \] \[{{t}_{2}}=\frac{12}{11+{{S}_{2}}}\] Also, \[{{t}_{1}}+{{t}_{2}}=2+\frac{45}{60}\] \[\Rightarrow \] \[\frac{12}{11-{{S}_{2}}}+\frac{12}{11+{{S}_{2}}}=2.75\] \[\Rightarrow \] \[12\left( \frac{22}{121-S_{2}^{2}} \right)=2.75\] \[\Rightarrow \] \[121-S_{2}^{2}=\frac{22\times 12}{2.75}\] \[\Rightarrow \] \[121=S_{2}^{2}=\frac{22\times 12}{2.75}\] \[\Rightarrow \] \[121-S_{2}^{2}=96\] \[\Rightarrow \] \[S_{2}^{2}=25\] \[\Rightarrow \] \[{{S}_{2}}=5\,\text{km/h}\]
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