A radioactive substance has a half-life of four months. Three fourth of the substance would decay in

1. Half-life is the time taken for half of a radioactive substance to decay. Here, the half-life is 4 months. 2. We want to find the time it takes for three-fourths (3/4) of the substance to decay. This means one-fourth (1/4) of the substance remains. 3. After one half-life (4 months), half (1/2) of the substance remains. 4. After two half-lives (4 months + 4 months = 8 months), half of the remaining half decays, leaving (1/2) * (1/2) = 1/4 of the original substance. 5. Since 1/4 remains, 3/4 has decayed. This takes two half-lives, which is 2 * 4 = 8 months.