Linear equations, solutions, roots of equations. Algebra IIM CAT, XAT Quant sample Questions : Ascent CAT Classes

Question 4 the day : April 02, 2003
The question for the day is a sample practice problem in Linear equation. Helps understand concepts related to formulating equations from a word problem and finding solution to the equations.

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 Chennai to Trivandrum costs Rs. 216 and 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?

1. Rs. 105 and Rs. 6
2. Rs. 216 and Rs. 12
3. Rs. 210 and Rs. 12
4. Rs. 210 and Rs. 6

Correct Answer is Rs. 210 and Rs. 6. Correct Choice is (4)

Explanatory Answer

Let half of the full basic fare be Rs. X.
Therefore, full basic fare is Rs. 2X.

Let the reservation charge be Rs. Y per ticket.
Now, one full reservation ticket would cost 2X (basic fare) + Y (reservation charge)
2X + Y = 216    --- (1)

The total basic fare for one half and one full ticket = X + 2X = 3X and the total reservation charge is 2Y.
Hence, 3X + 2Y = 327    --- (2)

Solving (1) and (2) we get,
X = 105 and Y = 6

Hence, the full basic fare is 2X = Rs. 210 and the reservation charge is Y = Rs. 6

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