Question

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 Ahmedabad costs Rs 216 and one full and one half reserved first class tickets cost Rs 327. What is the basic first class full fare and what is the reservation charge?

Answer 1

$\huge\mathcal{\underline{Question:-}}$

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 Ahmedabad costs Rs 216 and one full and one half reserved first class tickets cost Rs 327. What is the basic first class full fare and what is the reservation charge?

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$\huge\mathcal{\underline{Solution:-}}$

Let the cost of full fare be x and the reservation charge be y.

According to the question,

Case (i) x + y = 216 ---------------------- (1)

Case (ii) 3/2 x + 2y = 327

             ⇒ 3x + 4y = 654 ---------------------- (2)

By solving equations 1 and 2, we get

x = 210 and y = 6.

Therefore, fare for 1 ticket is Rs 210 and the reservation charges are Rs 6.

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Answer 2

Step-by-step explanation:

Let the cost of fare be rs.'x' and the reservation charge be rs.'y'.

By condition I:

x+y=216 ....(i)

By condition II:

(one full and one half ticket = 1+1/2 = 3/2)

(cost of half railway ticket is x/2)

therefore,

x+y+x/2+y=327

3/2x+2y=327

i.e. 3x+4y=654 ....(ii)(after multiplying by 2 )

by solving (i) and (ii)

you will get

x=210 and y=6

Hence, basic fare for one ticket is rs.210 and reservation fare is rs.6