The exact measure of money then vs now is not quite as easy as you might think. Now, most of the equivalents I have seen, and the ones I use most, indicate that 20 rubles in 1910 era would be the same as 200 US$ today. It may actually be a bit higher than that, given purchasing power and the shifting costs between goods and labor. Back then, labor was very cheap, and the goods were more expensive. Today, labor is very expensive comparatively and goods are less so. However, it should give you some idea.
For comparison sake, a room in the Hotel Europa, the best in Petersburg could be had for 1.50 rubles a night for the cheapest room, and dinner in the hotel restaurant was 2 rubles. (I daresay dinner at the Hotel Europa today will cost more than $20!) You could hire a carriage for an entire day for 10 rubles, and a carriage from a hotel to the theater and back including a stop for dinner at a restaurant was 3 rubles. So, 20 rubles had pretty decent purchasing power for "an allowance"