Today market was down but still calls and puts both has fallen, what is the reason and is this has any relation with india vix?

India vix is down 5 to 6% , thats why options whether call or putt both are down

Please refer section 19.4 - …you will get your answer.

what is the relationship ? between both …how it has effected the calls and puts.

option prices always depend on volatility sir, always check vix when you buy or write option