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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...
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 +
- 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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Community 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
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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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? for Class 10 2026 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 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? covers all topics & solutions for Class 10 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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