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A railway half ticket cost half the full fare and the reservation charge is the same on a half ticket as on a full ticket. one reserved first-class ticket from Delhi to Patna costs ₹ 216. One full and one half reserved first-class ticket cost ₹ 328. What is the reservation charge?
  • a)
    ₹ 16
  • b)
    ₹ 26
  • c)
    ₹ 6
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A railway half ticket cost half the full fare and the reservation char...
Let ₹ x be the charge of full first-class ticket and ₹ y be reservation charge.
x + y = 216 ...(1)
x + y + x/2 + y = 327
⇒ 3x + 4y = 654 ...(2)
By solving eqns (1) and (2), we get
x = 210, y = 6 
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Community Answer
A railway half ticket cost half the full fare and the reservation char...
Given:
- A full ticket fare is twice the fare of a half ticket.
- The reservation charge is the same for both full and half tickets.

To find:
The reservation charge.

Let's assume the full ticket fare as 'F' and the reservation charge as 'R'.

Case 1: One reserved first-class ticket from Delhi to Patna costs 216.
- Full ticket fare + Reservation charge = 216
- F + R = 216 ...(Equation 1)

Case 2: One full and one half reserved first-class ticket cost 328.
- Full ticket fare + Half ticket fare + Reservation charge = 328
- F + (F/2) + R = 328 ...(Equation 2)

We need to solve these two equations to find the values of F and R.

Solving the equations:
Multiply Equation 1 by 2 to eliminate the fraction in Equation 2.
2F + 2R = 432 ...(Equation 3)

Subtract Equation 2 from Equation 3 to eliminate F.
2F + 2R - (F + (F/2) + R) = 432 - 328
2F + 2R - F - F/2 - R = 104
3F/2 + R = 104 ...(Equation 4)

Substitute the value of F from Equation 1 into Equation 4.
3(216/2) + R = 104
3(108) + R = 104
324 + R = 104
R = 104 - 324
R = -220

Since the reservation charge cannot be negative, we made a mistake in our calculations. Let's reconsider the problem.

Correct Approach:
Let the full ticket fare be 'F' and the reservation charge be 'R'.

Case 1: One reserved first-class ticket from Delhi to Patna costs 216.
- Full ticket fare + Reservation charge = 216
- F + R = 216 ...(Equation 1)

Case 2: One full and one half reserved first-class ticket cost 328.
- Full ticket fare + Half ticket fare + Reservation charge = 328
- F + (F/2) + R = 328 ...(Equation 2)

We need to solve these two equations to find the values of F and R.

Solving the equations:
Multiply Equation 1 by 2 to eliminate the fraction in Equation 2.
2F + 2R = 432 ...(Equation 3)

Subtract Equation 2 from Equation 3 to eliminate F.
2F + 2R - (F + (F/2) + R) = 432 - 328
2F + 2R - F - F/2 - R = 104
3F/2 + R = 104 ...(Equation 4)

Multiply Equation 1 by 3 to eliminate R in Equation 4.
3F + 3R = 648 ...(Equation 5)

Subtract Equation 4 from Equation 5 to eliminate R.
3F + 3R - (3F/2 + R) = 648 - 104
3F +
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A railway half ticket cost half the full fare and the reservation charge is the same on a half ticket as on a full ticket. one reserved first-class ticket from Delhi to Patna costs 216. One full and one half reserved first-class ticket cost 328. What is the reservation charge?a) 16b) 26c) 6d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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