Let the count rate at zero time be K

Count rate after 3mins, = \(\frac{K}{2}\)

Count rate after 6mins =  \(\frac{K}{4}\)

but count after 6mins = 400 ( given )

Then =  \(\frac{K}{4}\) = 400

K = 4 X 400 = 1600

∴ = count rate at zero time = 1600.