Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is
A.$16\ ^2/_3\ \%$ B. $14\ ^1/_2\ \%$ C. $13\ ^1/_3\ \%$ D. $15\ \%$
First, please explain me the question, I didn't get the thus gaining 2% part.
On
$\newcommand{\angles}[1]{\left\langle\, #1 \,\right\rangle} \newcommand{\braces}[1]{\left\lbrace\, #1 \,\right\rbrace} \newcommand{\bracks}[1]{\left\lbrack\, #1 \,\right\rbrack} \newcommand{\ceil}[1]{\,\left\lceil\, #1 \,\right\rceil\,} \newcommand{\dd}{{\rm d}} \newcommand{\ds}[1]{\displaystyle{#1}} \newcommand{\expo}[1]{\,{\rm e}^{#1}\,} \newcommand{\fermi}{\,{\rm f}} \newcommand{\floor}[1]{\,\left\lfloor #1 \right\rfloor\,} \newcommand{\half}{{1 \over 2}} \newcommand{\ic}{{\rm i}} \newcommand{\iff}{\Longleftrightarrow} \newcommand{\imp}{\Longrightarrow} \newcommand{\pars}[1]{\left(\, #1 \,\right)} \newcommand{\partiald}[3][]{\frac{\partial^{#1} #2}{\partial #3^{#1}}} \newcommand{\pp}{{\cal P}} \newcommand{\root}[2][]{\,\sqrt[#1]{\vphantom{\large A}\,#2\,}\,} \newcommand{\sech}{\,{\rm sech}} \newcommand{\sgn}{\,{\rm sgn}} \newcommand{\totald}[3][]{\frac{{\rm d}^{#1} #2}{{\rm d} #3^{#1}}} \newcommand{\verts}[1]{\left\vert\, #1 \,\right\vert}$ $$ \mbox{Every month you pay}\quad 600\,{r/1200 \over 1 - \pars{1 + r/1200}^{-9}} = {688.50 \over 9} $$
$$ \mbox{From this equation, we'll get}\ \approx 34.13\ \%\ \mbox{per annum}. $$
Selling Price $$S.P.=102\%\times600=612 $$
Present Worth$$P.W.=612$$ and Sum$$S=688.5$$ True Discount$$T.D.=688.5-612=76.5$$ Thus, Simple Interest on $Rs. 612$ for $9$ months is $Rs. 76.50$
Therefore, Rate $$R=\frac{100\times76.5}{612\times\frac34}=16\frac23\%$$