CAT 2006 — QA Question 17
Answer the following question based on the information given below.
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.
What is the weight of Praja‘s luggage?
Answer & solution
- A
20 kg
- B
25 kg
- C
30 kg
35 kg
- E
40 kg
Let f kg be the free luggage allowance and let Raja and Praja have r kg and p kg excess luggage respectively.
Let x be the fixed rate per kg for excess luggage.
∴ 2f + r + p = 60 ... (i)
rx = 1200 ... (ii)
px = 2400 ... (iii)
(60 – f)x = 5400 ... (iv)
From (ii) and (iii),
p = 2r ... (v)
Substituting in (i),
2f + 3r = 60
∴ f = 30 – 3r/2 ... (vi)
Substituting in (iv),
(60 – 30 + 3r/2)x = 5400
∴ 30x + 3rx/2 = 5400
From (ii),
rx = 1200
∴30x = 3600
∴ x = 120
∴ r = 10, p = 20 and f = 15
∴ Weight of Praja's luggage = p + f = 35 kg
Hence, option (d).