£220 for alternator...am I being ripped off??

For once I have taken my car to an apparent MG garage because the alternator has gone and I can't do the work myself at the mo. Originally I was quoted by email £40 for the alternator and £40 for the work. I left it with the garage and they have now quoted me £220. Am I being ripped off because I'm a woman?? :crying:

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