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06 Aug 2022, 00:11
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
55% (03:37) correct
45%
(03:15)
wrong
based on 11
sessions
History
Date
Time
Result
Not Attempted Yet
Etihad Airways allows some free luggage. It charges for excess luggage at a fixed rate per kg. Two friends, A and B had 17 kg of luggage between them. They were charged Rs.3500 and Rs.2000 respectively for excess luggage. If the entire luggage belonged to one of them, the luggage charge would have been Rs.7000. What was the weight of the luggage of A(in kg)?
A. 8
B. 9
C. 10
D. 11
E. 12
(adapted from varsity tutors)
A. 8
B. 9
C. 10
D. 11
E. 12
(adapted from varsity tutors)
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06 Aug 2022, 00:42
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Etihad Airways allows some free luggage. It charges for excess luggage at a fixed rate per kg. Two friends, A and B had 17 kg of luggage between them. They were charged Rs.3500 and Rs.2000 respectively for excess luggage. If the entire luggage belonged to one of them, the luggage charge would have been Rs.7000. What was the weight of the luggage of A(in kg)?
Solution:-
here it can be using HCF properties as well as
They paid for extra Luggage
Let Rs A per kg for extra luggage
For A =3500/A
For B =2000/A
For Only one person=7000/A
here the answer will be the Common Factor of (3500,2000,7000) which i believe is 500
so A paid for extra luggage is 3500
Weight for extra weight is 7kg
and for B it is =2000/5=4kg
So ATQ the total weight between them is 17kg = 7+4+x+x
So X=3 kg
total weight A carries=10kg
answer is option C'
Solution:-
here it can be using HCF properties as well as
They paid for extra Luggage
Let Rs A per kg for extra luggage
For A =3500/A
For B =2000/A
For Only one person=7000/A
here the answer will be the Common Factor of (3500,2000,7000) which i believe is 500
so A paid for extra luggage is 3500
Weight for extra weight is 7kg
and for B it is =2000/5=4kg
So ATQ the total weight between them is 17kg = 7+4+x+x
So X=3 kg
total weight A carries=10kg
answer is option C'
25 Aug 2022, 23:21
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pintukr
Solution:
Method 1: Using logic
When splitting 17kgs between A and B: A pays 3500 and B pays 2000. Total charge for extra luggage = 3500 + 2000 = 5500
When any one of them carries the luggage: Total charge for extra luggage = 7000
Charge paid in the 2nd scenario is 1500 more because of the two discounts offered (allowance) in the 1st scenario
If this 1500 discount does not exist, each of A and B would have paid 3500 + 1500 = 5000 and 2000 + 1500 = 3500 respectively
Ratio \(= \frac{A}{B}=\frac{5000}{3500}=\frac{10}{7} \)
The weight carried by A \(= \frac{10}{10+7}\times 10=10\)
Method 2: Forming equation
Let's take a few variables:
\(x\): weight friend A is carrying
\(17-x\): weight friend B is carrying
\(F:\) weight that is free to carry
\(E\): extra money for each kg of extra weight
We can essentially make 3 equations:
Friend A getting charged 3500: \((x-F)\times E=3500.........(i)\)
Friend B getting charged 2000: \((17-x-F)\times E=2000.........(ii)\)
Any one of them getting charged 7000: \((17-F)\times E=7000............(iii)\)
\((i)÷(ii):\)
\(\frac{(x-F)\times E}{(17-x-F)\times E}=\frac{3500}{2000}⇒\frac{x-F}{17-x-F}=\frac{7}{4}⇒11x+3F=119......(iv)\)
\((i)÷(iii):\)
\(\frac{(x-F)\times E}{(17-F)\times E}=\frac{3500}{7000}⇒\frac{x-F}{17-F}=\frac{1}{2}⇒2x-F=17.......(v)\)
\(3\times (v)+(iv): \)
\(6x-3F+11x+3F=51-119⇒17x=170⇒x=10 \)
Hence the right answer is Option D
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
