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.

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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.

Rs. 1280

Rs. 2500

Rs. 3570

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 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.

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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