Problem Solving

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

Q1. what is the weight of pravin's luggage ?
(a) 20 kg
(b)25 kg
(c)30 kg
(d)35kg
(e)22 kg

Q2. what is the free luggage allowance?
(a) 10 kg
(b) 15 kg
(c) 20 kg
(d) 25 kg
(e)18 kg

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

Q1. what is the weight of pravin's luggage ?
(a) 20 kg
(b)25 kg
(c)30 kg
(d)35kg
(e)22 kg

(fixed weight + 1200 worth of excess weight) + (fixed weight + 2400 worth of excess weight) = 60
(x + y) + (x + 2y) = 60
2x + 3y = 60____________________(1)

(fixed weight) + (5400 worth of excess weight) = 60
x + (5400/1200) y = 60
x + 9y/2 = 60
2x + 9y = 120____________________(2)

(2) - (1):
6y = 60
y = 10
Put this in (1):
x = 15

Weight of Pravin's luggage = x + 2y = 15 + 20 = 35 kg

Choose D

abhasjha wrote:Q2. what is the free luggage allowance?
(a) 10 kg
(b) 15 kg
(c) 20 kg
(d) 25 kg
(e)18 kg

x = 15 kg

Choose B

Cheers

alt approach

1200->2400->5400
x = kg"s worth of 1200->2x = kg"s worth of 2400-> 3x+y = kg"s worth of 5400
extra kgs worth of 5400 = y+3x
y is the standard kgs which are free
now combined If all kgs would be with one of the person = 3600 + 1800 worth of Kgs
therefore y = 1.5x kgs
now 1.5x+x+1.5x+2x = 60,x=10
standard kgs =10
rakesh kgs = 10+15=25, praveen's kgs = 10+25 = 35

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

Q1. what is the weight of pravin's luggage ?
(a) 20 kg
(b)25 kg
(c)30 kg
(d)35kg
(e)22 kg

Q2. what is the free luggage allowance?
(a) 10 kg
(b) 15 kg
(c) 20 kg
(d) 25 kg
(e)18 kg

We can plug in the answers to Q2, which represent the free luggage allowance.
The total weight of all the luggage = 60kg.
The answer choices imply the following options for the total weight of the excess luggage:
60-10 = 50.
60-15 = 45.
60-20 = 40.
60-25= 35.
60-18 = 42.

Since the fee for one person traveling = 5400, the correct value for the excess luggage is almost certainly a factor of 5400.
Eliminate D and E, which are not factors of 5400.
Of the remaining answer choices, the middle value is the best place to start.
If answer choice B is incorrect, we'll be able to determine whether the correct answer choice must be smaller or greater.
When the correct answer choice is plugged in, the following constraint must be satisfied:
Rakesh's luggage + Pravin's luggage = 60kg.

Answer choice B: 15
Here, the charge per kg of excess luggage = 5400/45 = 120.

The following baggage weights are implied:
Rakesh:
Excess baggage weight = (total charge)/(fee per kg) = 1200/120 = 10kg.
Total baggage weight = free allowance + excess weight = 15+10 = 25.
Pravin:
Excess baggage weight = (total charge)/(fee per kg) = 2400/120 = 20kg.
Total baggage weight = free allowance + excess weight = 15+20 = 35.

Total weight for Rakesh and Pravin = 25+35 = 60kg.
Success!

Thus:
The correct answer to Q1 is [spoiler]D (35[/spoiler]).
The correct answer to Q1 is [spoiler]B (15)[/spoiler].

I thought of sharing a alternate approach to question number 1.

Praveen pays = 2400
rakesh pays = 1200

since Praveen pays more we can safely assume that Praveen has more luggage than rakesh .

If at all the luggage were equal they would be 30 kgs each ... but Praveen > rakesh ...which implies Praveen must be greater than 30. only one choice in question is greater than 30 ... which is option D ..... (35)

if Praveen is 35 then rakesh = 60-35 = 25 .

now use this data to find solution to question 2 .

This way you need not write equation and can save you some valuable time.....