[UPSC CSE 2020] Nuclear Physics (Q54, 10M)

Natural uranium found in the earth's crust contains the isotopes ^{235}_{92}\mathrm{U} and ^{238}_{92}\mathrm{U} in the atomic ratio 7\cdot3\times10^{-3} to 1. Assuming that at the time of formation these two isotopes were produced equally, estimate the time since formation. Given that the mean lives of both the isotopes are 1.03\times10^{9} years and 6.49\times10^{9} years, respectively.