Question

A train started from Station A, developed engine trouble, and reached Station B, 40 minutes late. What is the distance between Stations A and B? Statements: I. The engine trouble developed after travelling 40 km from Station A and the speed reduced to $\dfrac{1}{4}^{\text{th}}$ of the original speed.
II. The engine trouble developed after travelling 40 km from Station A in two hours and the speed reduced to $\dfrac{1}{4}^{\text{th}}$ of the original speed.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both the statements I and II are needed to answer the question.
• D. If the question cannot be answered even with the help of both the statements.

Hint:

When a question involves speed and delay, ensure time components can be equated with distances. Use both statements if they give complementary parts of the equation.

Answer 1

The Correct Option is C

From statement I:
The engine trouble developed after travelling 40 km, and speed dropped to $\dfrac{1}{4}$th of original. But no information is given about the time or original speed. Hence, Statement I alone is not sufficient. From statement II:
We know the train took 2 hours to travel 40 km before the breakdown. So, original speed = $\dfrac{40}{2} = 20$ km/hr. Post that, the speed became $\dfrac{1}{4} \times 20 = 5$ km/hr. But this statement does not mention how much distance was left to be covered at reduced speed. So Statement II alone is also not sufficient. Combining I and II:
- We get that 40 km was travelled in 2 hours at 20 km/hr. - After that, the remaining distance (say $x$ km) was travelled at 5 km/hr. - Total delay was 40 minutes or $\dfrac{2}{3}$ hour. Let total distance be $D$ km. \[ D = 40 + x \] Time taken to travel $x$ km at reduced speed: $\dfrac{x}{5}$ hours Time taken if there was no breakdown: $\dfrac{D}{20} = \dfrac{40 + x}{20}$ hours Total time with breakdown: $2 + \dfrac{x}{5}$ \[ \text{Delay} = \left(2 + \dfrac{x}{5}\right) - \dfrac{40 + x}{20} = \dfrac{2}{3} \] Solving this equation gives value of $x$, hence $D$ can be calculated. Thus, both statements together are sufficient.