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
$\frac{dP}{dt}=\frac{6}{100}P$
$\Rightarrow \underset{6000}{\overset{12000}{\int }}\frac{dp}{P}=\frac{3}{50}\underset{0}{\overset{t}{\int }}dt$
$\Rightarrow [\log P{]}_{6000}{}^{12000}=\frac{3}{50}t$
$\Rightarrow \log 12000-\log 6000=\frac{3}{50}t$
$\Rightarrow \log 2=\frac{3}{50}t$
$\Rightarrow t=\frac{50}{3}\log 2$