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Pair of Linear Equations in Two Variables | Pair of Linear Equations in Two Variables - Exercise 3.4

Question 9

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.

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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) }

⇒ (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 9

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.

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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) }

⇒ (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.

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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