A railway half-ticket costs half the full ticket. However the reservation charge for all the tickets is constant. One full reserved ticket for a journey is ₹525. If the cost of one full and one half reserved ticket for the same journey is ₹850, then what is the reservation charge per ticket?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹125
Every reserved ticket costs its fare plus the same reservation charge; a half ticket has half the fare but the full reservation charge.
Assuming the full fare to be \(F\) and the reservation charge \(R\):
One full ticket: \(F+R=525\) (1)
One full and one half ticket: \(\displaystyle F+\frac{F}{2}+2R=850\) (2)
Subtracting (1) from (2), the half ticket alone: \(\displaystyle\frac{F}{2}+R=325\) (3)
Subtracting (3) from (1), \(R\) cancels: \(\displaystyle\frac{F}{2}=200\), so \(F=400\)
Reservation charge \(R=525-400=125\)