At the beginning of the year 2019. India’s population was 130 crore and it is increasing at constant rate of 1% annually. Right now the mobile numbers are of 10 digits starting with digits 6, 7, 8 or 9 only as permitted by TRAI (a regulating body). The maximum number of years the current pattern of mobile numbers can run, assuming two mobile numbers per member of population $(u s e \log_{(1.01)} (\frac{20}{13}) = 43.29)$ is

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22 years

44 years

21 years

43 years

answer is B.

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Detailed Solution

Let $P_{0} = 130$ crore
After ‘n’ years population $P = P_{0} {(1 + 0.01)}^{n}$
Total number of possible mobile numbers $= 4 \times 10^{9} = 400 c r o r e$
Hence, $2 P \leq 400 c r o r e \Rightarrow 130 {(1.01)}^{n} \leq 200 \Rightarrow n \leq \log_{1.01} (\frac{20}{13}) = 43.29$
$\Rightarrow n \leq 43 y e a r s$

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