Question

Geetanjali Express, which is 250 m longer when moving from Howrah to Tatanagar, crosses Subarnarekha bridge in 30 seconds. What is the speed of Geetanjali Express?
 Statement I: Bombay Mail, which runs at 60 km/h, crosses the Subarnarekha bridge in 30 seconds.
Statement II: Bombay Mail, when running at 90 km/h, crosses a lamp post in 10 seconds.
 

• A. if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
• B. if the question can be answered by either statement alone.
• C. if the question can be answered by using both statements together, but cannot be answered using either statement alone.
• D. if the question cannot be answered even by using both the statements together.

Hint:

To compute speed, we need both time and total distance. If bridge length is known, time directly gives speed.

Answer 1

The Correct Option is A

We are to compute speed of Geetanjali Express, given: 
- It is 250 m longer than Bombay Mail 
- It takes 30 seconds to cross the same bridge

Statement I: Bombay Mail at 60 km/h (or \( \frac{60000}{3600} = 16.67 \) m/s) takes 30 seconds ⇒ Distance of bridge = \( 16.67 \times 30 = 500 \) m So bridge length = 500 m. Geetanjali Express takes 30 sec to cross it ⇒ It covers 750 m (250 m train + 500 m bridge) in 30 sec ⇒ Speed = \( \frac{750}{30} = 25 \) m/s = \( 90 \) km/h Thus, Statement I is sufficient alone. \medskip 

Statement II: Bombay Mail crosses lamp post in 10 sec at 90 km/h ⇒ train length = \( \frac{90 \times 1000}{3600} \cdot 10 = 250 \) m So we can compute Bombay Mail’s length, but nothing about bridge or Geetanjali Express. Not sufficient. \[ {\text{Option (a)}} \]