A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Mumbai to Ahmedabad costs Rs 216 and one full and one half reserved first class tickets cost Rs 327. What is the basic first class full fare and what is the reservation charge?

Question

Philoid · Accepted Answer

Let the basic full fare be ‘a’, half far be ‘b’ and reservation charges be ‘r’.

Given, railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket.

a = 2b ----- (1)

Also, reserved first class ticket from Mumbai to Ahmedabad costs Rs 216 and one full and one half reserved first class tickets cost Rs 327.

⇒ a + r = 216 ------ (2)

Also, a + b + 2r = 327 ----- (3)

Substituting value of a in eq2 and eq3

⇒ 2b + r = 216 and 3b + 2r = 327

Solving the above equations, we get

r = Rs. 6 and b = Rs. 105

Thus a = Rs. 210