Problem Solving

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

What is the free luggage allowance?
A) 10Kg
B) 15Kg
C) 20Kg
D) 25Kg
E) 30Kg

with my very rough paper work, with just the agenda/attempt to finding the correct answer - it seems answer should be B

post the correct answer

gmattarget700 wrote:with my very rough paper work, with just the agenda/attempt to finding the correct answer - it seems answer should be B

you could have takena snap of ur rough work and posted the soln here..
oreither could have written the ans..Well correct ans is B..

Let the free luggage allowance be x kg. The data is as below.

Free Allowance : Raja (x) Praja (x)


Excess : Raja ( a - x ) Praja (60 - a - x)
Praja pays Rs.2400 for 60 - a - x
Raja pays Rs.1200 for a - x
∴ 60 - a - x = 2(a - x)
⇒ 60 + x = 3a -----------------(i)
If the entire luggage belonged to, say Praja, he would have
to pay Rs.5400.

∴
(60 -a-ax)/(60-x)=2400/5400 = 4/9
⇒ 540 - 9a - 9x = 240 - 4x

⇒ 300 - 5x = 9a -------------(ii)
From (i) and (ii) x = 15 and a = 25
∴ Praja's luggage is 60 - 25 = 35 kg and the free allowance in 15 kg.

[spoiler]Hence (B)[/spoiler]