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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 Ahmadabad costs. Rs.216 while 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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Solution

## 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+12=32cost of half railway ticket is =x2∴,x+y+x2+y=327⇒32x+2y=327 ⇒3x+4y=654 ....(ii)(after multiplying by 2 )By solving (i) and (ii) we will get3x+4y−4x−4y=654−864∴x=210 and put x=210 in (i) we get y=216−x=216−210=6∴y=6Hence, basic fare for one ticket is Rs.210 and reservation fare is Rs.6

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