Question

Mr. Sharma and Mr. Arora are family friends and they decided to go for a trip. For the trip they reserved their rail tickets. Mr. Arora has not taken a half ticket for his child who is 6 year old whereas Mr. Sharma has taken half tickets for his two children who are 6.5 years and 8 years old. A railway half ticket costs half of the full fare but the reservation charges are the same as on a full ticket. Mr. and Mr. Arora paid 1700, while Mr. and Mrs. Sharma paid 2700. Find the full fare of one ticket and the reservation charges per ticket. ​

Answer 1

$\fbox{\texttt{\green{Answer:}}}$

Full fare of one ticket = Rs. 700

Reservation charge = Rs. 150

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Total amount paid by Mr. and Mrs. Arora = Rs. 1700

Total amount paid by Mr. and Mrs. Sharma = Rs. 2700

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1. Full far of one ticket.

2. Reseravtion charges per ticket.

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Let the reservation charges = Rs. x

Full fare charges = Rs. y

According to the question,

Mr. Arora paid Rs.1700 for 2 full tickets with reservation charges.

i.e., $\bold{2x+2y=1700}$

$\implies\bold{x+y=850\longrightarrow{(1)}}$

Mr. Sharma paid Rs. 2700 for 2 full tickets and for 2 half tickets along with reservation charges.

i.e., $\bold{4x+2y+2\times{}\frac{y}{2}=2700}$

$\implies\bold{4x+3y=2700\longrightarrow{(2)}}$

Now, $\bold{(1)\times{}4\implies\:4x+4y=3400\longrightarrow{(3)}}$

Subtracting $\bold{(2)}$ & $\bold{(3)}$, we get :-

$\bold{-y=-700}$

$\implies\bold{y=700}$

Substituting value of y in $\bold{(1)}$ :-

$\bold{x=850-700=150}$

i.e., Full fare of one ticket = Rs. 700

Reservation charge = Rs. 150