| A boat running upstream takes 528 min to cover a certain distance, while it takes 240 min to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current, respectively? |
A) 2: 1
B) 3: 2
C) 8: 3
D) Cannot be determined
E) None of these
Correct Answer: C
Solution :
| Let boat's rate upstream be x and |
| Boat's rate downstream \[=y\] |
| According to the question, |
| Distance covered in 528 min upstream |
| = Distance covered in 240 min downstream |
| \[\Rightarrow \]Distance covered in 8 h 48 min |
| = Distance covered in 4h |
| \[\Rightarrow \]\[x\times 8\frac{4}{5}=(y\times 4)\]\[\Rightarrow \]\[\frac{44}{5}x=4\]\[\Rightarrow \]\[y=\frac{11}{5}x\] |
| \[\Rightarrow \]Required ratio \[=\left( \frac{y+x}{2} \right):\left( \frac{y-x}{2} \right)\] |
| \[=\left( \frac{\frac{11}{5}x+x}{2} \right):\left( \frac{\frac{11}{5}x-x}{2} \right)=\left( \frac{16}{5}\times \frac{1}{2} \right):\left( \frac{6x}{5}\times \frac{1}{2} \right)\] |
| \[=\frac{8x}{5}:\frac{3x}{5}=8:3\] |
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