Probability exercise

Question

I have an exercise, where I now know the correct answer, but I just don't know how to get that result. This is the exercise:

I have tried using Bayes' Theorem, but I still cannot get the same result. Can you explain how it should be solved?

Answer 1

Let $d$ be the fraction of cars bought that are diesel. The fraction that are petrol is then $1-d$ The fraction sold after three years is $$0.515(1-d)+0.2d=0.3\\0.215=0.315d$$