cleetus wrote:
Spice Airline has a free luggage allowance of " f " kg. If any passanger carries excess luggage, it is charged at a constant rate per kg. The total luggage charge paid by two passangers, A and B is $1050. If each of A and B had carried twice the luggage he actually did, their luggage charges would have been $2400 and $900 respectively. Find A's luggage charge.
A) 750
B) 900
C) 1200
D) 1500
E) 1050
Its a bit time consuming problem but possible.
1st case: A's luggage charge + B's luggage charge = 1050
Therefore: (A-f)R + (B-f)R = 1050 (where f is the luggage allowed and R is the rate per extra luggage)
=> AR+BR-2fR = 1050 --- Eq(i)
2nd case: when the luggage of A and B is doubled
Therefore: (2A-f)R + (2B-f)R = 2400+900 (adding the extra charge paid by A and B when luggage was doubled)
=> 2AR+2BR-2fR = 3300 --- Eq(ii)
solving eq 1 and eq 2 we get:
=> AR + BR = 2250
Substituting this value in eq 1 we get:
=> 2250-2fR = 1050
=> fR = 600
As we know (2A-f)R = 2400 and (2B-f)R = 900
therefore by replacing fR in the above eq, we get AR = 1500 and BR = 750
Now the question asks "What is the charge paid by A" that means the amount paid by A for the extra luggage
i.e. (A-f)R => AR-fR => 1500-600 => 900. (Substituting the value of AR and fR from above in the eq)
Hence B.