Question

3.) 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 Bokaro Steel City to New Delhi costs Rs 324 and one full and one half-reserved first class ticket cost Rs 496. What is the basic first-class full fare and what is the reservation charge ?

( Ans: 304, 20 )

Class 10

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Answer 1

Let the price full ticket be X
price for half ticket is X/2

Let the reservation price be Y

from first condition.
X+Y=324

from the second condition

X+(X/2)+2Y= 496

on solving the simultaneous equation.

X=304. Y=20

Answer 2

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Let the cost of the basic first class full fare be Rs.x and the reservation charge be Rs.y.

Then ATQ,

CASE 1, x + y = 324

=> x = 324 - y -----------(1)

CASE 2, x + 2y + x/2 = 496

=> 2x + 4y + x = 992

=> 3x + 4y = 992

Substituting (1) in above equation

=> 3(324 - y) + 4y = 992

=> 972 - 3y + 4y = 992

=> y = 20 <<<<<<< Answer

Using y in (1)

=> x = 324 - 20

=> x = 304 <<<<<<<<<< Answer

Thus the full first class train cost is Rs.304 and the reservation charge is Rs.20.

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