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Airline Excess Luggage Allowance

CAT 2006 Slot 1 · Quantitative Ability · Medium · Quantitative Aptitude

This is a medium Quantitative Ability question set from the CAT 2006 Slot 1 paper. It tests Quantitative Aptitude. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Passage / data set

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs 1200 and Rs 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs 5400.

Question 1 of 2

What is the weight of Praja's luggage?

  1. A.

    20 kg

  2. B.

    25 kg

  3. C.

    30 kg

  4. D.

    35 kg

  5. E.

    40 kg

Answer

35 kg

Explanation

Let free allowance be FF kg and rate per kg be VV. Raja excess charge: (x−F)V=1200(x - F)V = 1200. Praja excess charge: (60−x−F)V=2400(60 - x - F)V = 2400. Single person excess charge: (60−F)V=5400(60 - F)V = 5400.

Dividing Praja by Raja: 60−x−Fx−F=2  ⟹  60−x−F=2x−2F  ⟹  3x−F=60\frac{60 - x - F}{x - F} = 2 \implies 60 - x - F = 2x - 2F \implies 3x - F = 60. Dividing total by Raja: 60−Fx−F=4.5  ⟹  60−F=4.5x−4.5F  ⟹  4.5x−3.5F=60\frac{60 - F}{x - F} = 4.5 \implies 60 - F = 4.5x - 4.5F \implies 4.5x - 3.5F = 60. Solving 1.5×(3x−F=60)  ⟹  4.5x−1.5F=901.5 \times (3x - F = 60) \implies 4.5x - 1.5F = 90. Subtracting: 2F=30  ⟹  F=152F = 30 \implies F = 15 kg. 3x−15=60  ⟹  3x=75  ⟹  x=253x - 15 = 60 \implies 3x = 75 \implies x = 25 kg (Raja's luggage). Praja's luggage =60−25=35= 60 - 25 = 35 kg.

Question 2 of 2

What is the free luggage allowance?

  1. A.

    10 kg

  2. B.

    15 kg

  3. C.

    20 kg

  4. D.

    25 kg

  5. E.

    30 kg

Answer

15 kg

Explanation

From the system of equations derived above, F=15F = 15 kg.

Why the other options are wrong

  • A.10 kg — does not satisfy the condition asked in this question, so it is not the correct answer.
  • B.15 kg — does not satisfy the condition asked in this question, so it is not the correct answer.
  • C.20 kg — does not satisfy the condition asked in this question, so it is not the correct answer.
  • D.25 kg — does not satisfy the condition asked in this question, so it is not the correct answer.
  • E.30 kg — does not satisfy the condition asked in this question, so it is not the correct answer.

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