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# 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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This is the basic and exam oriented question from linear equations in two variables in which we have to find the cost of reservation charge and the basic first class full fare if 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.

Kindly solve the above problem

RS Aggarwal, Class 10, chapter 3E, question no 41

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1. Let cost of full fare ticket be Rs x and reservation charge be Rs y.
As per the statement, “One reserved first class ticket from Mumbai to Ahmedabad costs Rs. 216.” =>x+y=216 — (1)

And, “one full and one half reserved first class ticket cost Rs. 327=>(x+y)+(x/2+y)=327=>3x/2+2y=327 —           (2)

Multiplying equation  (1) with 2 we get, 2x+2y=432 —– equation (3)

Subtracting equation (2) from (3), we get 2x=105=>x=210
Substituting x=210 in the equation (1), we get 210+y=216=>y=6

Hence, cost of full far ticket is Rs 210 and reservation charge is Rs 6

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