1000 Rs. is invested at 5% per annum simple interest. If the interest is added to the principal after every 10 years, the amount will become 2000 Rs. after :
[A]$15\ years$
[B]$16\frac{2}{3}\ years$
[C]$18\ years$
[D]$20\ years$

$\mathbf{16\frac{2}{3}}\ years$
After 10 years
$SI = \frac{1000\times 5\times 10}{100} = 500\ Rs.$
Principal for 11th year = 1000 + 500 = 1500 Rs.
$\therefore T = \frac{SI\times 100}{P\times R} = \frac{500\times 100}{1500\times 5}$
$= \frac{20}{3}\ years = 6\frac{2}{3}\ years$
∴ Total time $= 10+6\frac{2}{3} = 16\frac{2}{3}\ years$
Hence option [B] is correct answer.