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# Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?

Option :

Explanation:

Solution:
$\begin{array}{rl}& \text{S}\text{.I}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{on}\phantom{\rule{thinmathspace}{0ex}}\text{Rs}\text{.}\phantom{\rule{thinmathspace}{0ex}}\left(\text{260 - 20}\right)\phantom{\rule{thinmathspace}{0ex}}\text{for}\phantom{\rule{thinmathspace}{0ex}}\text{a}\phantom{\rule{thinmathspace}{0ex}}\text{given}\phantom{\rule{thinmathspace}{0ex}}\text{time}\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}20.\\ & \text{S}\text{.I}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{on}\phantom{\rule{thinmathspace}{0ex}}\text{Rs}\text{.}\phantom{\rule{thinmathspace}{0ex}}\text{240}\phantom{\rule{thinmathspace}{0ex}}\text{for}\phantom{\rule{thinmathspace}{0ex}}\text{half}\phantom{\rule{thinmathspace}{0ex}}\text{time}\\ & =Rs.10.\\ & T.D.\phantom{\rule{thinmathspace}{0ex}}on\phantom{\rule{thinmathspace}{0ex}}Rs.\phantom{\rule{thinmathspace}{0ex}}250=Rs.10.\\ & \therefore T.D.\phantom{\rule{thinmathspace}{0ex}}on\phantom{\rule{thinmathspace}{0ex}}Rs.\phantom{\rule{thinmathspace}{0ex}}260\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}\left(\frac{10}{250}×260\right)\\ & =Rs.\phantom{\rule{thinmathspace}{0ex}}10.40\end{array}$