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 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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basic fare for one ticket is Rs.210 and reservation fare is Rs.8

basic fare for one ticket is Rs.310 and reservation fare is Rs.8

basic fare for one ticket is Rs.210 and reservation fare is Rs.6

basic fare for one ticket is Rs.110 and reservation fare is Rs.6

answer is C.

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Detailed Solution

Let cost of fare =x
Reservation charge =y
Now, sum of fare and reservation charge is 216. Thus,

x + y = 216

…. (1)
Multiply this equation with 4,

4 x + 4 y = 864

…. (2)
Half ticket cost

= \frac{x}{2}

. Here, total cost of one full and one-half ticket is 327. Thus,

x + y + \frac{x}{2} + y = 327

\frac{3}{2} x + 2 y = 327

3 x + 4 y = 654

.... (3)
Subtract equation 3 from 2,

3 x + 4 y - 4 x - 4 y = 654 - 864

x = 210

Put value of x in equation 1

y = 216 - x

y = 216 - 210

y = 6

Thus, basic fare for one ticket is Rs. 210 and reservation fare is Rs. 6
Correct option is 3.

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