Urban Fuel Services supplies three farms on the outskirts of the town with their fuel needs. It receives the farms' deliveries once a month and stores the fuel in 6 tanks of different sizes, reserved exclusively for the farms. Five of the tanks hold diesel and the sixth holds a petrol-alcohol mixture. The capacities of the tanks are, in no particular order, 20, 16, 15, 19, 18, and 31 gallons.
Some of the diesel is bought by Farmer A, and the balance - exactly twice as much - is bought by Farmer B. The blend is entirely for Farmer C.
All three farmers turned up to collect their supplies, as luck would have it, on a day when Mrs Worrier had been put in charge of the garage. She had not been told which tank contained which fuel, and neither she nor the farmers had any means of measuring the fuel, since the containers in which the farmers carried off their supplies were in all cases larger in capacity than the fuel they carried away and were not calibrated in any way. Nevertheless, when the farmers turned up, she was able to work out which tank held the blend and to fill the other two orders correctly.
And was insufferably smug for the rest of the day...
How did she do it?
First law of radiography: The colder the X-ray table, the more of your body is required on it.