Q.107. A railway half ticket costs half of the full fare and the reservation charges are the same on half as on full ticket. One reserved 3 A.C. class tickets from New Delhi to Lucknow costs Rs. 538 and one-half reserved 3 A.C. class ticket costs 294. Find the full basic fare and the charges separately
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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?
December 20, 2019avatar
Kinjal Mahender
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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+
2
1
=
2
3
cost of half railway ticket is =
2
x
∴,x+y+
2
x
+y=327
⇒
2
3
x+2y=327
⇒3x+4y=654 ....(ii)(after multiplying by 2 )
By solving (i) and (ii) we will get
3x+4y−4x−4y=654−864
∴x=210 and put x=210 in (i) we get y=216−x=216−210=6
∴y=6
Hence, basic fare for one ticket is Rs.210 and reservation fare is
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Answer:
Let the reservation charges be Rs.r and cost of full ticket of first class be Rs. y. It is given that one reserved first class ticket from the station A to B costs Rs. 2530. Also, one reserved first class ticket and one reserved first class half ticket from A to B costs Rs. 3810, therefore, a+y= 2530. .(1) and since railway half ticket costs half the full fare, but the reservation charges are the same on a half ticket as on a full ticket so we get (z + y) - (r+ ) = 3810 = dr +3y = 7620......(2) Multiplying equation 1 by 3 we get. 3r - 3y = 7590. . (3) Now subtracting equation 3 from equation 2, we get a = 30. Now substitute the value ofa in equation 1 that is: 30 +y = 2530 implies y = 2500 Hence, the full first class fare from station A to B is Rs. 2500.
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