Question

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 ₹ 216 and one full and one half reserved first class tickets cost ₹ 327. What is the basic first class full fare and what is the reservation charge?

Answer 1

Given:

Let the basic full first-class fare = ₹ x.

Reservation charge per ticket = ₹ y.

A half ticket costs half the full fare `(₹ x/2)` and has the same reservation charge y.

One reserved first-class ticket costs ₹ 216 ⇒ x + y = 216.

One full and one half reserved first-class tickets together cost ₹ 327 ⇒ `x + y + (x/2) + y = 327`.

Step-wise calculation:

1. From the first equation: x + y = 216   ...(Equation 1)

2. From the second: `x + y + x/2 + y = 327` 

⇒ `(3x)/2 + 2y = 327`   ...(Equation 2)

3. Express y from (Equation 1):

y = 216 – x

4. Substitute into (Equation 2):

`(3x)/2 + 2(216 - x) = 327` 

⇒ `(3x)/2 + 432 - 2x = 327`

⇒ `((3x)/2 - 2x) = 327 - 432 = -105`

⇒ `(3x - 4x)/2 = -105`

⇒ `(-x)/2 = -105`

⇒ `x/2 = 105`

⇒ x = 210

5. Then y = 216 – x

= 216 – 210

= 6

Basic full first-class fare = ₹ 210.

Reservation charge = ₹ 6.