The answer is.... 36 to 1! Did you get it right? Here’s how to solve the problem. The first pair of gears has a worm gear on the input axle and a 24 tooth gear on the output axle. This results in a gear ratio of 24 to 1. 
The second pair of gears has a 40 tooth gear meshed with another 40 tooth gear. In this case, the gear ratio is very simple. 40 to 40 simplifies to 1 to 1. 
The third pair of gears has a 16 tooth gear on the input axle, which is the same axle as the 40 tooth output gear from the second pair. It is meshed with an 8 tooth gear on the output axle. The gear ratio for this pair is 8 to 16 or 1 to 2. 
The final pair of gears has an 8 tooth gear on the input axle meshed with a 24 tooth gear on the output axle. This gear ratio is 24 to 8, or 3 to 1 after simplifiying. 
Let’s multiply all 4 gear ratios together to get the overall gear ratio of the compound gear train. 24 / 1 x 1 / 1 x 1 / 2 x 3 /1 = 36 / 1 This means that it takes 36 revolutions of the very first input axle, which contains the worm gear, to make 1 revolution of the very last output axle, which contains the 24 tooth gear. Build it and see for yourself!

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See also: Gears, Spur gear, Bevel gear, Worm gear, Idler gear, Gearbox, Belts and Pulleys