# 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.

### Mohammed

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get 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. from screen.

## 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 .

Click here👆to get an answer to your question ✍️ 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 .

Question

## 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.

**A**

## Rs. 1280

**B**

## Rs. 2500

**C**

## Rs. 3570

**D**

## Rs. 2250

Medium Open in App Solution Verified by Toppr

Correct option is B)

Step-1: Assume the required unknown to be equal to some variables

$$\textbf{& then apply all information's given.}$$

Let the reservation charges be Rs. x and cost of full ticket of first class be Rs. y

It is given that 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, therefore,

x+y=2530..........(1) and

since railway half ticket costs half the full fare, but the reservation charges are the same

on a half ticket as on a full ticket. So, we get,

(x+y)+(x+ 2 y )=3810

⇒4x+3y=7620.............(2)

Step-2: Simplify unknown.

Multiplying equation 1 by 3, we get,

3x+3y=7590..........(3)

Now subtracting equation 3 from equation 2, we get x=30.

Now substitute the value of x in equation 1 that is:

30+y=2530 ⇒ y=2500

Hence, the full first class fare from station A to B is Rs. 2500

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## A railway half ticket costs half the full fare but the reservation charges are the same on a half ti...

Free solutions for Mathematics Exemplar Problems - class 10 Chapter 4 - Pair of Linear Equations in Two Variables Pair of Linear Equations in Two Variables - Exercise 3.4 question 9. These explanations are written by Lido teacher so that you easily understand even the most difficult concepts

## NCERT Exemplar Solutions Class 10 Mathematics Solutions for Pair of Linear Equations in Two Variables - Exercise 3.4 in Chapter 3 - Pair of Linear Equations in Two Variables

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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 ₹ 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs ₹ 3810. Find the full first class fare from station A to B, and also the reservation charges for a ticket.

Answer:

Let the cost of full fare from station A to B = ₹ xand the reservation charges per ticket = ₹ y Cost of one full ticket from A to B = ₹ 2530

i.e., (1 fare + 1 reservation) charges = ₹ 2530

i.e., x + y = 2530

Cost of 1 full and one, half ticket from station A to B = ₹3810 i.e., (1 full ticket) + (1/2 ticket) charges = ₹3810 i.e., (x + y) + (1/2 fare + reservation) = 3810

(x+y)+\frac{1}{2} x+y=3810 \\ \Rightarrow \frac{3}{2} x+2 y=3810 \\ \Rightarrow 3 x+4 y=7620 \ldots \text { (ii) }

(x+y)+ 2 1 x+y=3810 ⇒ 2 3 x+2y=3810 ⇒3x+4y=7620… (ii)

⇒ (i), by 3, we get 3x + 3y = 7590 …(iii) Subtracting (iii) from (ii), we get

y = 30

Now, x + y = 2530 [From (i)]

⇒ x + 30 = 2530 (₹ y = 30) ⇒ x = 2530 – 30

⇒ x = ₹2500

Hence, full fare and reservation charges of a ticket station A to B are ₹2500 and ₹30 respectively.

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## Question 10 A railway half ticket cost half the full fare bu the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the stations A to B costs Rs. 2530. Also, one reserved first class ticket and one reserved first class half ticket from stations A to B costs Rs. 3810. Find the full first class fare from stations A to B and also the reservation charges for a ticket.

Question 10 A railway half ticket cost half the full fare bu the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the stations A to B costs Rs. 2530. Also, one reserved first class ticket and one reserved first class half ticket from stations A to B costs Rs. 3810. Find the full first class fare from stations A to B and also the reservation charges for a ticket.

Byju's Answer Standard X Mathematics Dividend Question 10 A... Question Question 10

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

Open in App Solution

Let the cost of full and half first class fare be Rs. x and Rs.

x 2

respectively and reservation I charges be Rs. Y per ticket.

Case I The cost of one reserved first class ticket from the stations A to B

= Rs 2530 ⇒ x + y = 2530

Case II The cost of one reserved first class ticket and one reserved first class half ticket from stations A to B = Rs. 3810

⇒ x + y + x 2 , + y = 3810 ⇒ + 2y = 3810 ⇒ 3x + y = 7620

Now, multiplying Eq. (i) by 4 and then subtracting from Eq. (ii), we get

3x + 4y = 7620 4x + 4y = 10120 - x = - 2500 ⇒ x = 2500

On putting the value of x in Eq. (i), we get

2500 + y = 2530 ⇒ y = 2530 – 2500 ⇒ y = 30

Hence, full first class fare from stations A to B is Rs. 2500 and the reservation for a ticket is Rs. 30.

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SIMILAR QUESTIONS

**Q.**

**Question 10**

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

**Q.**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 .

**Q.**A railway half ticket costs half the full fare but the reservation charges are the same for half ticket as well as for full ticket. One reserved first class ticket for a journey between two stations costs Rs. 378 and one full and one half reserved first class tickets cost Rs. 576. The reservation charges are:

**Q.**A half - ticket issued by railway costs half the full fare but the reservation charge is the same on half ticket as on full - ticket. One full reserved first class ticket for a journey between two stations costs Rs. 362 and one full and one half reserved first class ticker costs Rs. 554. The reservation charge is

**Q.**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 Ahmadabad costs.

R s .216

while one full and one half reserved first class tickets cost

R s .327

. What is the basic first class full fare and what is the reservation charge?

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