Question

In a bank, the principal increases continuously at the rate of $6 \%$ per year. Then the time required to double $6000$ rupees is__________ (in years)

• A. $\frac{50}{3} \log 2$
• B. $\frac{50}{3} \log 6$
• C. $\frac{50}{3} \log 3$
• D. $\frac{50}{3} \log 12$

Answer 1

Answer: (A)

According to given information, let the principal $P=₹ 6000$ getting double in time ' $t$ ' with rate of $6 \%$ per year, so
$\frac{d P}{d t}=\frac{6}{100} P$
$\Rightarrow \int\limits_{6000}^{12000} \frac{d p}{P}=\frac{3}{50} \int\limits_{0}^{t} d t$
$\Rightarrow [\log P]_{6000}{ }^{12000}=\frac{3}{50} t$
$\Rightarrow \log 12000-\log 6000=\frac{3}{50} t$
$\Rightarrow \log 2=\frac{3}{50} t$
$\Rightarrow t=\frac{50}{3} \log 2$