An isotope of potassium K⁴⁰ undergoes two parallel types of decay, one by electron capture and other by $\mathrm{\beta }$ decay with half lives as 1.3 x 10⁹  years and $\frac{1.3}{9}\times {10}^9$. If in a sample of a mineral, mass ratio of K : Ar : Ca is 5,1.5 and 16 then calculate age of the mineral if it is known that all Ca⁴⁰ in the mineral is not from the radioactive decay of potassium.

[Express your answer in terms of 10⁷ years for e.g. if you answer is 2 x 10⁹ years fill 0200 in OMR sheet]