Question:
A man walking upward on a staircase at the speed of x steps per second takes a total time of y seconds to reach the top. At what speed (in steps per second) he should walk to reach at the top in \(\frac{y}{3}\) seconds?
A man walking upward on a staircase at the speed of x steps per second takes a total time of y seconds to reach the top. At what speed (in steps per second) he should walk to reach at the top in \(\frac{y}{3}\) seconds?
Updated On: Mar 5, 2025
- \(\frac{3}{x}\)
- \(\frac{3x}{2}\)
- \(2x\)
- \(3x\)
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The Correct Option is D
Solution and Explanation
Step 1: Calculate the Number of Steps
The number of steps taken to reach the top is:
\[ \text{Number of steps} = x \times y \]
Step 2: Determine the New Speed
To cover the same number of steps in \(\frac{y}{3}\) seconds, the new speed must be:
\[ \text{New speed} = \frac{\text{Total steps}}{\text{Time taken}} \]
\[ = \frac{x \times y}{\frac{y}{3}} \]
Conclusion:
The required speed is \(3x\) steps per second.
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