A freshly prepared radioactive source of half life 2 hours 30...

Given here, $T = 150$ minutes,

${A}_{0} = 64x$, where, $x$ is the safe limit.

Using radioactive decay law relation, $A = {A}_{0} \times 2\dfrac{- t}{T}$, where, $t$ is the minimum time in hours after which it would be possible to work safely with source.

Putting the values, we have

$x = 64x \times 2\dfrac{- t}{T}$

$∴ t = 6T = 6 \times 2 . 5 = 15$ hours