Question

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 h less for the journey. What is the speed (in km/h) of the train?

• A. 40
• B. 30
• C. 20
• D. 10

Hint:

Plug in the options! $360/40 = 9$ hours. $360/45 = 8$ hours. The difference is 1 hour.

Answer 1

The Correct Option is A

Step 1: Concept
Time is equal to Distance divided by Speed ($T = D/S$).

Step 2: Analysis
Let the original speed be $x$ km/h. Original time $T_1 = 360/x$. New speed $x+5$, so New time $T_2 = 360/(x+5)$.

Step 3: Reasoning
Given $T_1 - T_2 = 1$:
$\frac{360}{x} - \frac{360}{x+5} = 1$
$360(x+5 - x) = x(x+5)$
$1800 = x^2 + 5x \Rightarrow x^2 + 5x - 1800 = 0$
$(x+45)(x-40) = 0$. Since speed cannot be negative, $x = 40$.

Step 4: Conclusion
The speed of the train is 40 km/h. Note: While the text mentions 20, the official key (2233) and calculation confirm 40. Final Answer: (A)