JEE Advanced 2019 Paper 1

In a radioactive sample, ‌1940K nuclei either decay into stable ‌2040Ca nuclei with decay constant 4.5×10−10 per year or into stable ‌1840 Ar nuclei with decay constant 0.5×10−10 per year. Given that in this sample all the stable ‌2040Ca and ‌1840 Ar nuclei are produced by the ‌1940K nuclei only. In time t×109 years, if the ratio of the sum of stable ‌2040Ca and ‌1840 Ar nuclei to the radioactive ‌1940K nuclei is 99, the value of will be : [Given ln‌10=2.3 ]