The half life of a radioactive substance is 20 minutes. The time taken between 50 $%$ decay and 87.5 $%$ decay of the substance will be

25 minutes

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30 minutes

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10 minutes

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40 minutes

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Solution

The correct option is D
40 minutes

$t_{2} - t_{1} = \frac{T}{I n 2} l n (\frac{N_{1}}{N_{2}}) = \frac{20}{I n 2} I n (\frac{50}{12.5}) = \frac{20}{I n 2} I n 4 = 40 m i n$

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