Question

Each of the following questions is followed by two statements, I and II. Decide whether the data given in the statements is sufficient to answer the question.

Geetanjali Express, which is 250 metres long, crosses the Subarnarekha bridge in 30 seconds while moving from Howrah to Tatanagar. What is the speed of Geetanjali Express?

I. Bombay Mail, which runs at 60 km/hour, crosses the Subarnarekha bridge in 30 seconds.
II. Bombay Mail, running at 90 km/hour, crosses a lamp post in 10 seconds.

• A. If Statement I alone is sufficient to answer the question.
• B. If Statement II alone is sufficient to answer the question.
• C. If Statement I and Statement II together are sufficient, but neither statement alone is sufficient to answer the question.
• D. If either Statement I alone or Statement II alone is sufficient to answer the question.

Hint:

Use the lamp post statement to find Bombay Mail's own length, then use the bridge-crossing statement to find the bridge length; only then can Geetanjali's speed be found.

Answer 1

The Correct Option is C

Step 1: Identify what is missing.
Geetanjali Express is 250 m long and crosses the bridge in 30 s. To cross a bridge, a train must cover its own length plus the bridge length, so
\[ \text{Speed of Geetanjali} = \frac{250 + L}{30} \]
where \(L\) is the length of the Subarnarekha bridge, which is not yet known.

Step 2: Test Statement I alone.
Statement I says Bombay Mail (60 km/hr) crosses the same bridge in 30 s. But Bombay Mail's own length is not known, so we cannot separate Bombay Mail's length from the bridge length using this one equation. Statement I alone is not sufficient.

Step 3: Test Statement II alone.
Statement II says Bombay Mail (90 km/hr) crosses a lamp post, a point object, in 10 s. This gives Bombay Mail's own length:
\[ 90 \text{ km/hr} = 25 \text{ m/s}, \quad \text{length} = 25 \times 10 = 250 \text{ m} \]
This tells us Bombay Mail's length but nothing about the bridge or Geetanjali Express. Statement II alone is not sufficient.

Step 4: Combine both statements.
From Statement II, Bombay Mail is 250 m long. From Statement I, Bombay Mail (60 km/hr = 16.667 m/s) crosses the bridge in 30 s, covering its own length plus the bridge:
\[ 16.667 \times 30 = 500 \text{ m} = 250 + L \implies L = 250 \text{ m} \]
Now the bridge length is known, so Geetanjali's speed is
\[ \frac{250 + 250}{30} = \frac{500}{30} = 16.667 \text{ m/s} = 60 \text{ km/hr} \]
Only by using both statements together do we get a number.

Final Answer:
Neither statement alone gives the bridge length, but together they do, so the correct choice is C. \[ \boxed{C} \]