The correct option is (c) same as
For explanation: For PFR, (frac{τ}{CA0} = int_0^{XA}frac{dXA}{-rA} )
For Batch reactor, (frac{t}{CA0} = int_0^{XA}frac{dXA}{-rA} )
From the above equations it is clear that theoretically the element of fluid reacts for same length of time in PFR and Batch reactor. But shutdown time as to be considered for actual design.