The ones I always used to struggle with were those that involved calculating the position that things will meet. For example, car leaves point A and travels towards point B at 20mph, at the same time, a cyclist leaves point B and travels towards A at 8 mph. The distance between A and B is 70 miles. Where will they cross?
The motorist is travelling two and a half times faster than the cyclist, (20/8 =2.5) so for every 10 miles travelled by the motorist, the cyclist travels 4. The trick is to ADD the ratio of speeds together (2.5+1=3.5), then divide the total distance by the ratio. 70/3.5 =140/7=20. The cyclist will travel 1 x 20 miles, whilst the motorist travels 2.5 x 20 miles (50 miles).
I wondered at the time what the aim of these questions was, but consider the following:
Target ac 800 nm away, approaching at 400knots, fighter travels at 540 knots but takes 15 mins to get airborne after scramble. What time do we scramble to meet the target at the edge of our Air Policing Area (say) 250 nm out? It is 1200Z, allow 15 minutes launch time. For the purpose of the exercise, there is no significant wind. You may use a calculator. Answers on a postcard please ....
I also remember at Biggin Hill being presented with a theoretical problem that I had to work on then present a verbal solution to the Boarding Officers. It involved transport and distance calcs as above, but my solution ended with an MP being picked up from the train station on the back of a motorbike. Not ideal, but it worked ... right up to the moment when the Wg Cdr pointed out that the MP was Margaret Thatcher! The only response I had was '******'.