### CAT 2006 Question Paper Question 3

Instructions

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 3

# What is the weight of Praja’s luggage?

Solution

Let the limit be x and the rate of charge be k per kg.
Let the excess luggage with Raja be R kg.
So, excess luggage with Praja = 2R kg
Now, excess luggage with Raja + excess luggage with Praja = 60 - 2x
So, 3R = 60 - 2x => R = 20 - 2x/3 which was charged 1200 Also, if one person had the entire luggage, excess luggage would have been 60 - x, which would have been charged 5400.
So the charge for the excess of (20-$$\frac{2x}{3}$$) = k(20-$$\frac{2x}{3}$$) = 1200  ....(1)
Also, the charge for the excess of 60-x = k(60-x) = 5400 .....(2)
Dividing (1) by (2), we get
=>$$\frac{\left(60-2x\right)}{3\times\ \left(60-x\right)}=\frac{1200}{5400}$$
Solving this, x = 15 kg
So, Praja's luggage = 35 kg