The mean lives of radioactive substance are 1620 year and 405 year for $\;\alpha\;$ emission and $\;\beta\;$ emission respectively . Find time during which $\;{\large\frac{3}{4}}^{th}\;$ of a sample will decay if it is decaying both by $\;\alpha\;$ emission and $\;\beta\;$ emission simultaneously .

Question

$(a)\;469 years\qquad(b)\;512 years \qquad(c)\;449 years \qquad(d)\;412 years$