The mean lives of a radioactive substance are 1620 years and 405 years of `alpha`-emission and `beta`-emission respectively. Find out the time during which three-fourth of a sample will decay if it is decaying both by `alpha`-emission and `beta`-emission simultaneously.

Explanation

To solve the problem step by step, we will follow the outlined process to find the time during which three-fourths of a sample will decay when it is decaying by both alpha-emission and beta-emission simultaneously.

### Step 1: Determine the decay constants for alpha and beta emissions.

The mean life (τ) is related to the decay constant (λ) by the formula:
\[ \lambda = \frac{1}{\tau} \]
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