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If 60% of the downstream speed of a boat is the same as the upstream speed of the boat. The speed of stream is what percentage of the speed of the boat in still water?
- a)20
- b)25
- c)30
- d)40
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If 60% of the downstream speed of a boat is the same as the upstream s...
Understanding Boat Speeds
To analyze the problem, let’s define some variables:
- Let the speed of the boat in still water be \( B \).
- Let the speed of the stream be \( S \).
Speed Relations
The downstream speed of the boat is given by:
- Downstream Speed = \( B + S \)
The upstream speed of the boat is:
- Upstream Speed = \( B - S \)
According to the problem, 60% of the downstream speed equals the upstream speed:
Formulating the Equation
We can set up the equation:
\[ 0.6 \times (B + S) = B - S \]
Solving the Equation
Expanding and simplifying the equation:
1. \( 0.6B + 0.6S = B - S \)
2. Rearranging gives:
- \( 0.6B + 0.6S + S = B \)
- \( 0.6B + 1.6S = B \)
3. Simplifying further:
- \( 1.6S = B - 0.6B \)
- \( 1.6S = 0.4B \)
4. Dividing both sides by \( B \):
- \( \frac{S}{B} = \frac{0.4}{1.6} \)
- \( \frac{S}{B} = \frac{1}{4} \)
Calculating Percentage
This means:
- \( S = \frac{1}{4}B \)
To express \( S \) as a percentage of \( B \):
- \( \frac{S}{B} \times 100 = 25\% \)
Conclusion
Thus, the speed of the stream is **25%** of the speed of the boat in still water. Hence, the correct option is **B**.
To analyze the problem, let’s define some variables:
- Let the speed of the boat in still water be \( B \).
- Let the speed of the stream be \( S \).
Speed Relations
The downstream speed of the boat is given by:
- Downstream Speed = \( B + S \)
The upstream speed of the boat is:
- Upstream Speed = \( B - S \)
According to the problem, 60% of the downstream speed equals the upstream speed:
Formulating the Equation
We can set up the equation:
\[ 0.6 \times (B + S) = B - S \]
Solving the Equation
Expanding and simplifying the equation:
1. \( 0.6B + 0.6S = B - S \)
2. Rearranging gives:
- \( 0.6B + 0.6S + S = B \)
- \( 0.6B + 1.6S = B \)
3. Simplifying further:
- \( 1.6S = B - 0.6B \)
- \( 1.6S = 0.4B \)
4. Dividing both sides by \( B \):
- \( \frac{S}{B} = \frac{0.4}{1.6} \)
- \( \frac{S}{B} = \frac{1}{4} \)
Calculating Percentage
This means:
- \( S = \frac{1}{4}B \)
To express \( S \) as a percentage of \( B \):
- \( \frac{S}{B} \times 100 = 25\% \)
Conclusion
Thus, the speed of the stream is **25%** of the speed of the boat in still water. Hence, the correct option is **B**.
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Community Answer
If 60% of the downstream speed of a boat is the same as the upstream s...
60% of downstream speed = Upstream speed
Downstream speed : Upstream speed = 100 : 60 = 5 : 3
Stream speed : Speed of the boat in still water
Hence, Option B is correct.
Downstream speed : Upstream speed = 100 : 60 = 5 : 3
Stream speed : Speed of the boat in still water
Hence, Option B is correct.
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If 60% of the downstream speed of a boat is the same as the upstream speed of the boat. The speed of stream is what percentage of the speed of the boat in still water?a)20b)25c)30d)40Correct answer is option 'B'. Can you explain this answer?
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