Question

Three trains-Rajdhani Express, Shatabdi Express and Taj Mahal Express-travel between two stations without stopping anywhere in between. No two trains have the same starting station or the same terminating station or the same travel fare. Also, the following known about these trains.

• A. The fare for the train which travels between Chennai and Pune is 1650.
• B. \rupee 1650
• C. \rupee 1800
• D. \rupee 1050

Hint:

Use variable substitution and equations to decode multiple constraints. Eliminate impossible assignments and confirm consistency with locations.

Answer 1

The Correct Option is B

Step 1: Extract all clues
We are told:
[(i)] The fare for the train between Chennai and Pune is \rupee 1650
[(ii)] Taj Mahal Express runs between Delhi and Mumbai
[(iii)] Fare for Bengaluru–Agra train is \rupee 750 less than Taj Mahal Express
[(iv)] Fare for Rajdhani Express is \rupee 150 less than Taj Mahal Express Step 2: Assign train identities and equations
Let us assume: \[ \text{Fare of Taj Mahal Express} = x \] Then:
Bengaluru–Agra train fare = \( x - 750 \)
Rajdhani Express fare = \( x - 150 \) Only one of the above trains can be Chennai–Pune, with fare \rupee 1650. Try assigning: \[ x - 750 = 1650 \Rightarrow x = 2400 \] Then: \[ \text{Taj Mahal Express} = 2400, \quad \text{Rajdhani} = 2250, \quad \text{Shatabdi} = 1650 \] Now check if the assignments match the cities:
Taj Mahal = Delhi–Mumbai (✓)
Then, Bengaluru–Agra must be Shatabdi (✓)
Chennai–Pune must be the remaining → Rajdhani (✓) Thus, \[ \text{Fare of Shatabdi Express} = \boxed{\rupee 1800} \]