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?

Explanation:-

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,\left( {{\text{260 - 20}}} \right)\,{\text{for}}\,{\text{a}}\,{\text{given}}\,{\text{time}} \cr & = Rs.\,20. \cr & {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{240}}\,{\text{for}}\,{\text{half}}\,{\text{time}} \cr & = Rs.10. \cr & T.D.\,on\,Rs.\,250 = Rs.10. \cr & \therefore T.D.\,on\,Rs.\,260 \cr & = Rs.\,\left( {\frac{{10}}{{250}} \times 260} \right) \cr & = Rs.\,10.40 \cr}$$