A) 8km/h
B) 3km/h
C) 5km/h
D) 11km/h
Correct Answer: A
Solution :
| Let the speed of the boat in still water |
| = x km/h |
| and the speed of the stream = y km/h |
| \[\therefore \] The speed of the boat upstream |
| = (x - y) km/h |
| and the speed of the boat downstream |
| =(x + y)km/h |
| Time taken to go 35 km upstream |
| \[=\frac{35}{x-y}h\] |
| Time taken to go 55 km downstream |
| \[=\frac{55}{x+y}h\] |
| According to the question, |
| \[\frac{35}{x-y}+\frac{55}{x+y}=12\] (i) |
| and \[\frac{30}{x-y}+\frac{44}{x+y}=10\] ...(ii) |
| Substituting \[\left( x\text{ }-\text{ }y \right)=a\] and \[\left( x\text{ }+\text{ }y \right)\text{ }=\text{ }b,\] |
| we get |
| \[\frac{35}{a}+\frac{55}{b}=12\] (iii) |
| and \[\frac{30}{a}+\frac{44}{b}=10\] (iv) |
| Multiplying Eq. (iii) by 6 and Eq. (iv) by 7, |
| we get |
| \[\frac{210}{a}+\frac{330}{b}=72\] (v) |
| And \[\frac{210}{a}+\frac{308}{b}=70\] (iv) |
| Subtracting Eq. (vi) from Eq. (v), we get |
| \[\frac{22}{b}=2\] |
| \[\Rightarrow \,\,\,2b=22\] |
| \[\Rightarrow \,\,\,\,b=11\] |
| From Eq. (iii), |
| \[\frac{35}{a}+\frac{55}{11}=12\] |
| \[\Rightarrow \,\,\,\,\frac{35}{a}+5=12\] |
| \[\Rightarrow \,\,\,\frac{35}{a}=7\] |
| \[\Rightarrow \,\,\,\,7a=35\] |
| \[\Rightarrow \,\,\,a=5\] |
| Hence, \[a=x-y=5\] (vi) |
| and \[b=x+y=11\] ...(iv) |
| Solving Eqs. (vii) and (viii), we get |
| \[x=8,\,y=3\] |
| \[\therefore \] The speed of the boat in still water |
| =8km/h |
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