`(m_(A))/(m_(B)) = (100)/(1),(M_(A))/(M_(B)) = (1.02)/(1)`
`bar(T_(A))=4 xx10^(9) year, bar(T_(B)) = 2xx10^(9)year`
At `t = 0, ((N_A)_(0))/((N_B)_(0)) =(1)/(1)`
`t = t, (N_(A))/(N_(B)) = (m_(A)//M_(A))/(m_(B)//M_(B)) = (m_(A))/(m_(B)).(M_(B))/(M_(A))`
`= (100)/(1)xx(1)/(1.02) = (100)/(1.02)`
`lambda_(A) = (1)/(bar(T_(A))) = (1)/(4xx10^(9)) year^(-1), lambda_(B) = (1)/(2xx10^(9))year^(-1)`
`N_(A) = (N_A)_(0)e^(-lambda_(A)t)`
`N_(B) = (N_B)_(0)e^(-lambda_(B)t)`
`(N_(A))/(N_(B)) = e(lambda_(B)-lambda_(A))t`
`(100)/(1.02) = e^(((1)/(2xx100^(9))-(1)/(4xx10^(9)))t) =e^((t)/(4xx10^(9))`
`ln((100)/(1.02)) = (t)/(4xx10^(9))`
`t= 4 xx 10^(9) xx 4.58`
`= 1.83 xx 10^(10)year`