A) 2 km/h
B) 3 km/h
C) 4 km/h
D) 5 km/h
Correct Answer: C
Solution :
| [c] Let speed of boat in still water = u km/h and speed of stream = v km/h Then, \[\frac{25}{u-v}+\frac{39}{u+v}=11\] ...(i) and \[\frac{35}{u-v}+\frac{52}{u+v}=11\] ...(ii) Multiplying Eq. (i) by 4 and Eq. (ii) by 3 and subtracting Eq. (ii) from Eq. (i), we get \[\frac{100}{u-v}-\frac{105}{u-v}=32-33\] \[\Rightarrow \] \[\frac{-5}{u-v}=-1\] \[\Rightarrow \] \[u-v\] Now, from Eq. (i), we get \[\frac{25}{5}+\frac{39}{u+v}=8\] \[\Rightarrow \] \[\frac{39}{u+v}=8-5=3\] \[\Rightarrow \] \[u+v=13\] (iv) Now, subtracting Eq. (iv) from Eq. (iii), we get \[(u-v)-(u-v)=5-13\] \[\Rightarrow \] \[-\,2v=-\,8\] \[\Rightarrow \] \[v=4\,km/h\] |
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