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 be loged to one of them, the excess luggage charge would have been rs 5400.
Answers
Given : 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 be loged to one of them, the excess luggage charge would have been rs 5400.
To Find : Weight of raja and Praja
Charges per kg for extra weight
Solution:
Let say x kg was allowed free
charges per kg for extra luggage = Rs y
Raja Weight = A kg
Praja Weight = 60 - A kg
Raja charges = (A - x) y = 1200
Praja charges = (60-A - x)y = 2400
=> (60 - A - x)/ (A - x) = 2
=> 60 - A - x = 2A - 2x
=> 3A = x + 60
entire luggage to one the charges
(60- x) * y = 5400
(60 - x)/(A - x) = 5400/1200
=> 360 - 6x = 27A - 27x
=> 27A = 21x + 360
27A = 21x + 360
3A = x + 60 => 27A = 9x + 540
=> 12x = 180 => x = 15
A = 25 kg
Raja Weight = 25 kg
Praja Weight = 35 kg
(A - x) y = 1200 => y = 120 Rs per kg
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