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PS Question need solution explanation

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PS Question need solution explanation  [#permalink]

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New post 19 Jul 2011, 14:33
00:00
A
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Question Stats:

100% (00:53) correct 0% (00:00) wrong based on 2 sessions

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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

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Re: PS Question need solution explanation  [#permalink]

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New post 19 Jul 2011, 19:57
1
what is the source of the problem? the #s are not adding up.. or probably the wordings are not very easy to understand..
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Re: PS Question need solution explanation  [#permalink]

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New post 19 Jul 2011, 21:00
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.
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Re: PS Question need solution explanation  [#permalink]

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New post 21 Jul 2011, 09:26
Sudhanshuacharya wrote:
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.


Thanks Sudhanshuacharya. Great help. Real solution explanation in the source is time consuming and difficult to understand
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Re: PS Question need solution explanation  [#permalink]

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New post 21 Jul 2011, 19:11
yeah its lengthy. I gave up at one point almost ..but finally got the answer.
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Re: PS Question need solution explanation  [#permalink]

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New post 22 Jul 2011, 05:50
esbee wrote:
yeah its lengthy. I gave up at one point almost ..but finally got the answer.


If u practice 10 such questions by taking ample time, u can pace it in less than 2 mins

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Re: PS Question need solution explanation  [#permalink]

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New post 21 Oct 2018, 11:48
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Re: PS Question need solution explanation &nbs [#permalink] 21 Oct 2018, 11:48
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