Question

Write 'T' for true and 'F' for false

(i) Simple interest on Rs x for x years is Rs x. Then, the rate of interest is x% per annum.
(ii) Rate = $\frac{100\times \mathrm{SI}}{P\times T}$.
(iii) A sum doubles itself at simple interest at 10% per annum in 10 years.
(iv) Simple interest on Rs 1000 at 5% per annum for 73 days is Rs 10.

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{False} \\ S.I.=\frac{P\times R\times T}{100} \\ \Rightarrow x=\frac{x\times R\times x}{100} \\ \Rightarrow R=\frac{100\times x}{x\times x} \\ \Rightarrow R=\frac{100}{x}\% \\ \left(\mathrm{ii}\right)\mathrm{True} \\ \left(\mathrm{iii}\right)\mathrm{True} \\ \mathrm{Let}\mathrm{the}\mathrm{sum}\mathrm{be}\mathrm{Rs}x. \\ \mathrm{S}.\mathrm{I}.=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{T}}{100} \\ \mathrm{S}.\mathrm{I}.=\frac{\mathrm{x}\times 10\times 10}{100} \\ \mathrm{S}.\mathrm{I}.=\mathrm{Rs}x \\ \mathrm{Amount}=\mathrm{S}.\mathrm{I}.+\mathrm{P} \\ =\mathrm{x}+\mathrm{x} \\ =\mathrm{Rs}2\mathrm{x} \\ \left(\mathrm{iv}\right)\mathrm{True} \\ \mathrm{P}=\mathrm{Rs}1000,\mathrm{R}=5\%,\mathrm{T}=73\mathrm{days}=\frac{73}{365}\mathrm{yrs} \\ \mathrm{S}.\mathrm{I}.=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{T}}{100} \\ =\frac{1000\times 5\times 73}{100\times 365} \\ =\mathrm{Rs}10 \end{gathered}$$