Chosen Solution

My speakers/microphone i.e. audio input output stopped working all of a sudden. When went to an apple service center they told me to replace the whole motherboard itself which is really expensive.

mmm … That’s odd, your system uses a daughter board called the ‘I/O board’ which has the headphone jack and the DAC unit which converts the digital signal to an analog signal (bi-directionally). I would replace it first if you don’t have any signs of liquid damage or didn’t bang your system. Here’s the IFIXIT guide and part: MacBook Air 13" Early 2014 I/O Board Replacement and the part MacBook Air 13" (Mid 2013 through Early 2015) I/O Board - Apple P/N 923-0439 If you click on the parts second image you can see the Cirris DAC chip just behind the headphone jack. You may want to replace the I/O cable if you think you banged your bottom cover as sometimes the bang can damage the cable.

change your input settings and then try to plug it in