Etihad Airways allows some free luggage. It charges for excess luggage

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