Question:hard

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.

Show 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.
Updated On: Jul 10, 2026
  • If Statement I alone is sufficient to answer the question.
  • If Statement II alone is sufficient to answer the question.
  • If Statement I and Statement II together are sufficient, but neither statement alone is sufficient to answer the question.
  • If either Statement I alone or Statement II alone is sufficient to answer the question.
Show Solution

The Correct Option is C

Solution and Explanation

Step 1: List the unknowns.
There are three unknowns: the bridge's length, Bombay Mail's length, and Geetanjali's speed. Geetanjali's own length (250 m) and crossing time (30 s) are given, but the bridge length is missing, so its speed cannot be pinned down yet.

Step 2: Check Statement II by itself.
A lamp post has no length, so distance covered equals the train's own length. At 90 km/hr = 25 m/s for 10 s, Bombay Mail's length is $25 \times 10 = 250$ m. This finds Bombay Mail's length only and says nothing about the bridge or Geetanjali. Not sufficient alone.

Step 3: Check Statement I by itself.
Statement I says Bombay Mail at 60 km/hr crosses the bridge in 30 s. This single equation mixes two unknowns, Bombay Mail's length and the bridge's length, so it cannot be solved alone. Not sufficient alone.

Step 4: Combine the two statements.
Statement II gives Bombay Mail's length as 250 m. Feed this into Statement I: 60 km/hr $= \frac{50}{3}$ m/s, and in 30 s Bombay Mail covers $\frac{50}{3} \times 30 = 500$ m. This distance is Bombay Mail's length plus the bridge length, so the bridge is $500 - 250 = 250$ m long.

Step 5: Now solve for Geetanjali's speed.
Geetanjali covers $250 + 250 = 500$ m in 30 s, giving a speed of $\frac{500}{30} = \frac{50}{3}$ m/s, which is 60 km/hr.

Final Answer:
The bridge length, and hence Geetanjali's speed, can only be found using both statements together, so the answer is C. \[ \boxed{C} \]
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