From the given kinetic energy of the neutrons we first calculate their velocity. Thus

         $\frac{1}{2}{\mathit{\text{mv}}}^2=0\text{.}0327\times 1\text{.}6\times 10^{-19}$

∴       $v^2=\frac{2\times 0\text{.}0327\times 1\text{.}6\times 10^{-19}}{1\text{.}675\times 10^{-27}}=625\times 10^4$

or       $v = 2500 \mathrm{m} {\mathrm{s}}^{-1}$

With this speed, the time taken by the neutrons to travel a distance of 10 m is,

          $\Delta t=\frac{10}{2500}=4\times 10^{-3} \mathrm{s}$

The fraction of neutrons decayed in time Δt second is,

          $\frac{\Delta N}{N}=\lambda \Delta t$

Also,   $\lambda =\frac{0\text{.}693}{T_{1/2}}$

$\therefore \; \; \; \frac{\Delta N}{N}=\frac{0\text{.}693}{T_{1/2}}\Delta t=\frac{0\text{.}693}{700}\times \left(4\times 10^{-3}\right)=3\text{.}96\times 10^{-6}$