(what i did), first i calculated n i.e. 13*17,
then z = (p-1)*(q-1) = 12*16= 192.
to find private key from given public key i.e. e=35 we need to find d which satisfy the equation
e*d = 1(mod z) or e*d mod z =1
i focused on z = 192, and try to find which multiple of 192 can give remainder 1 when divided by 35 , luckily i got 192*2= 385
which satisfy 35*11 mod 192 =1.
mp point here is instead of doing a lengthy work, try the simple one GATE will not try to test your calculation skill