a) 1 year
b) 6 months
c) 3 months
d) $$1\frac{1}{2}$$ years

Answer: b
Explanation:
$$\eqalign{ & P = Rs.\,3300 \cr & A = Rs.\,3399 \cr & R = 6\% \,{\text{per}}\,{\text{annum}} \cr & {\text{Let}}\,{\text{the}}\,{\text{time}}\,{\text{be}}\,{\text{n}}\,{\text{years}}{\text{.}} \cr & {\text{Compound}}\,{\text{interest}}\,{\text{is}}\,{\text{taken}}\,{\text{half – yearly}}. \cr & A = P \times {\left[ {1 + \left( {\frac{R}{2} \times 100} \right)} \right]^{2n}} \cr & 3399 = 3300{\left( {1 + \frac{3}{{100}}} \right)^{2n}} \cr & {\left( {1.03} \right)^{2n}} = \frac{{3399}}{{3300}} \cr & {\left( {1.03} \right)^{2n}} = {\left( {1.03} \right)^1} \cr & Thus,\,2n = 1\,year \cr & n = \frac{1}{2}{\text{year}} = 6\,{\text{months}} \cr} $$