Two passengers boarding a flight were found to have between them 34.5 kg of luggage. As per the excess luggage policy of the flight operator, the two passengers were made to pay Rs. 3.75 and Rs. 6.00 for the excess weight of their luggage. Later they found out that if the same luggage were to belong to just one person, then the excess luggage fee would have been Rs. 13.50. How much free luggage is allowed for each passenger?

Let the luggage weight of passenger 1 be x kg, and that of passenger 2 be y. 

Also, let the free luggage allowance be F and the charge per kg on the luggage over the free allowance be C. 

We know that x + y  = 34.5 kg

Case 1: The total excess fee is Rs. 3.75 + Rs. 6 = Rs. 9.75.

The individual excess weights are (x−F) and (y−F)

(x−F)*C+(y−F)*C = 9.75

(x+y−2F)*C = 9.75 or we can say, (34.5−2F)*C = 9.75.........(Eq. 2)

Case 2: Luggage Belongs to One Person (Rs. 13.50)

(34.5 − F)*C = 13.50 (Eq. 3)

Dividing Eq. 2 by Eq. 3

$$\dfrac{(34.5−F)C}{(34.5−2F)C​}=\dfrac{13.50}{9.75}​$$

$$\dfrac{(34.5−F)}{(34.5−2F)​}=\dfrac{13.50}{9.75}​$$

18*(34.5 − 2F) = 13*(34.5−F)

18 × 34.5 − 36F = 13 × 34.5 − 13F

(18 − 13) × 34.5 = 36F − 13F

5 × 34.5 = 23F

172.5 = 23F

F = 7.5 Kg