Half lives of two radioactive substances P and Q are 10 minutes and 20 minutes respectively. Initially the samples of P and Q have equal number of nuclei. Then after 60 minutes, the ratio of numbers of decayed nuclei in the samples of P and Q is

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9 : 8

9 : 7

8 : 7

5 : 7

answer is D.

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Detailed Solution

$\frac{N_{0} - N_{P}}{N_{0}} = 1 - \frac{N_{P}}{N_{0}} = 1 - \frac{1}{{(2)}^{60 / 10}} = 1 - \frac{1}{2^{6}} = \frac{63}{64}$

$Similarly, \frac{N_{0} - N_{Q}}{N_{0}} = 1 - \frac{N_{Q}}{N_{0}} = 1 - \frac{1}{{(2)}^{60 / 20}} = \frac{7}{8}$

$∴ \frac{N_{0} - N_{P}}{N_{0} - N_{Q}} = \frac{63}{64} x \frac{8}{7} = \frac{9}{8}$

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