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A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810. Find the full first class fare from station A to B, and also the reservation charges for a ticket

Solution:

Consider the cost of full first class be ₹x

Consider the cost of half first class to be ₹ x/2.

The reservation charges are ₹ y per ticket.

Case I :

From station A to B, one reserved first class ticket cost = ₹2530

x + y = 2530-------------------------(1)

Case II :

From stations A to B, one reserved first class ticket and one reserved first class half ticket cost = ₹3810

x + y + x/2 + y = 3810

3x/2 + 2y = 3810

3x + 4y = 7620-----------------------(2)

Solve the linear equations (1) and (2)

Multiplying (1) by 4 and then subtracting from (2),we get,

(3x + 4y) - (4x + 4y) = 7620 - 10120

-x = -2500

x = 2500.

Substituting the value of x in (1),we get,

2500 + y = 2530

y = 2530 - 2500

y = 30.

So we get

x = 2500.

y = 30.

Therefore, full first class fare from stations A to B is ₹2500 and the reservation charge for the ticket is ₹30.

✦ Try This: A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs Rs 2500. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3800. Find the full first class fare from station A to B, and also the reservation charges for a ticket

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.4 Problem 10

A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810. Find the full first class fare from station A to B, and also the reservation charges for a ticket

Summary:

A railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the station A to B costs Rs 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs 3810. The full first class fare from stations A to B is ₹2500 and the reservation charge for the ticket is ₹30

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