A train covers 400 km at a uniform speed. If the speed had been 10 km/h more, it would have taken 2 hours less for the same journey. What is the usual time taken (in hours) by it to complete the journey?
This questions was previously asked in
SBI PO Prelims
Explanation:
- Let the usual speed be \( x \) km/h.
- Then, the usual time taken is \( \frac{400}{x} \) hours.
- With the increased speed (\( x + 10 \) km/h), time taken becomes \( \frac{400}{x + 10} \) hours.
- Given that the increased speed reduces travel time by 2 hours, we have:
\[
\frac{400}{x} - \frac{400}{x + 10} = 2
\]
- Solving the equation, cross-multiply and simplify:
\[
400(x + 10) - 400x = 2x(x + 10)
\]
\[
4000 = 2x^2 + 20x
\]
\[
x^2 + 10x - 2000 = 0
\]
- Solve this quadratic equation using the quadratic formula, \(\left(\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\right)\), where \( a = 1, b = 10, c = -2000 \).
- The solution gives two values for \( x \), and the relevant one plugged back into \(\frac{400}{x}\) gives 10 hours.
- Option 4: 10 is correct.
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By: Parvesh Mehta