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# The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is:

Option :

Explanation:

Solution:
$\begin{array}{rl}& \text{Let}\phantom{\rule{thinmathspace}{0ex}}\text{P}\text{.W}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{be}\phantom{\rule{thinmathspace}{0ex}}\text{Rs}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{x}\text{.}\\ & \text{Then,}\phantom{\rule{thinmathspace}{0ex}}\text{S}\text{.I}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{on}\phantom{\rule{thinmathspace}{0ex}}\text{Rs}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{x}\phantom{\rule{thinmathspace}{0ex}}\text{at}\phantom{\rule{thinmathspace}{0ex}}\text{16}\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{for}\phantom{\rule{thinmathspace}{0ex}}\text{9}\phantom{\rule{thinmathspace}{0ex}}\text{months}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}189.\\ & \therefore x×16×\frac{9}{12}×\frac{1}{100}\\ & =189\phantom{\rule{thinmathspace}{0ex}}or\phantom{\rule{thinmathspace}{0ex}}x=1575.\\ & \therefore P.W.=Rs.\phantom{\rule{thinmathspace}{0ex}}1575.\\ & \therefore \text{Sum}\phantom{\rule{thinmathspace}{0ex}}\text{due}=P.W.+T.D.\\ & =Rs.\left(1575+189\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}1764.\end{array}$