Question
The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:
Answer: Option D
$$\eqalign{
& P.W. = Rs.\left( {1760 - 160} \right) = Rs.\,1600 \cr
& \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{at}}\,{\text{12}}\% \,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{160}}{\text{}} \cr
& \therefore {\text{Time}} = {\frac{{100 \times 160}}{{1600 \times 12}}} \cr
& = \frac{5}{6}{\text{years}} \cr
& = \left( {\frac{5}{6} \times 12} \right){\text{months}} \cr
& = 10\,{\text{months}}{\text{}} \cr} $$
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$$\eqalign{
& P.W. = Rs.\left( {1760 - 160} \right) = Rs.\,1600 \cr
& \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{at}}\,{\text{12}}\% \,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{160}}{\text{}} \cr
& \therefore {\text{Time}} = {\frac{{100 \times 160}}{{1600 \times 12}}} \cr
& = \frac{5}{6}{\text{years}} \cr
& = \left( {\frac{5}{6} \times 12} \right){\text{months}} \cr
& = 10\,{\text{months}}{\text{}} \cr} $$
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