Hello all just a quick query on this question below which has got me a little confused. The question asks what is the maximum passenger weight that may be carried in Row 2 at take-off. I understand the process but when the question asks about take-off weight shouldn't the fuel be considered in the calculations? The workings to the question I've attached below to this just consider ZFW items. In this regard shouldn't the question be asking what the maximum passenger weight that may be carried in row 2 at ZFW be? Why is fuel not considered here is my question? Cheers.
Given:

Aircraft empty weight.............689 kg
Empty aircraft index units........19522
Oil............................... 7 kg
Row 1 pilot and passenger.........110 kg
Baggage (baggage compartment).....75 kg
Fuel............................. 140 litres

The maximum passenger weight, in kg, that may be carried in Row 2 at take-off is closest to ....... kg

Edit: Problem resolved

Just a comment: you may have sourced a solution to your question but, if you had the problem, chances are that others will have some as well. Always better to field a suitable answer for the benefit of the group.

Possibly you need to review the W&B stuff a bit more. I get the impression that you are trying to run problems as by rote techniques rather than sitting back and having a bit of a head scratch about what the question is setting out to achieve.

We note that

(a) the initial load gives a CG of 2927.4 mm which is likely to present an aft limit problem for the final loading

(b) the aft limit is constant at 3004 mm.

(c) the R2 arm (3600) is aft of the aft limit (3004) so any R2 load is going to move the CG back towards the aft limit

(d) the fuel arm (2950) is forward of the aft limit so it isn't going to present any major problems, assuming that we keep a weather eye on gross weight limits along the way

As the aft limit is constant we are only concerned with what happens as we load up R2 and the ZFW CG moves closer to the aft limit.

Several ways to approach this but they all relate, effectively, to ballasting R2 to arrive at the aft limit. Then, as you add fuel from the aft limit ZFW loading, you move forward from the aft limit while, at the same time, making sure that you don't end up outside the limit should you, for some strange reason, run out of gas.

My answer comes up to be 113 kg to keep the roundoff inside the envelope. As to which the examiner wants, depends on how particular the examiner may be.

Apologies. Noted for future posts. You explained it a whole lot better than I would have explained it so thank you. I sat the exam last week and got 2 Charlie questions pretty much identical to this one just with different numbers of course. Came out with 86%.

I know it's not related to this post but thought I might share it anyway to benefit others if they see this. The exam for me consisted of around,
- 5-6 echo questions
- 2 Charlie questions both like the one above
- I got no alpha or bravo questions weirdly enough
- 4-5 fuel questions (working minimum fuel, safe endurance)
- A few endurance questions (How long you could hold for before diverting and how long you could spend out in a search area)
- 4 Take-off and landing chart questions
- Around 6-7 1-marker questions
- 2 PNR questions and 2 ETP questions (Remember to check for ETAS)
- A few easy questions on new fwd limit, MAC%, Density height, climb gradient

The exam in total had 34 questions if my memory serves me well

Hopefully, this helps anyone preparing and wondering what the exam may consist of.