A flask is filled with equal moles of A and B. The half lives of A and B are 100s and 50s respectively and are independent of the initial concentration. The time required for the concentration of A to be four times that of B is ______________s.

(Given : In 2 = 0.693)

Process is based upon simultaneous disintegration hence,

$\frac{0.693}{100}*t=2.303lo{g}_{10}\frac{A_0}{A_t}$ ………….(i)

and       $\frac{0.693}{50}*t=2.303lo{g}_{10}\frac{B_0}{B_t}$              ………….(ii)

from equation (i) and (ii)

$0.693t\left[\frac{1}{50}-\frac{1}{100}\right]=\left[log\frac{B_0}{B_t}-log\frac{A_0}{A_t}\right]*2.303$  

Here; A₀ = B₀ and $A_t=4*B_t$  

Therefore  $0.693t\left[\frac{1}{100}\right]=2.303\left[log\left(\frac{B_0}{B_t}*\frac{A_t}{A_0}\right)\right]$  

$\therefore t=\frac{2.303*0.3010*2*100}{693}=200s$