The master and the apprentice produce a batch of parts. The parts produced by the apprentice account for two fifths of the total number of parts. If the apprentice gives the master 15 parts, the ratio of the number of parts produced by the apprentice and the master is 1:3. How many parts are there in total?

The ratio of the number of parts produced by the apprentice and the master is 1:3, that is, the number of parts produced by the apprentice is 1 / 4 of the total,
The apprentice gave the master 15 pieces, and the number of parts decreased from 2 / 5 to 1 / 4
15, 2 / 5-1 / 4 = 3 / 20
The total number is 15 / (2 / 5-1 / 4) = 100

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