Question
A sum of money at simple interest doubles in 7 years. It will become four times in:
Answer: Option B
$$\eqalign{
& {\text{Let sum}} = {\text{Rs}}{\text{. }}x \cr
& {\text{Then,}} \cr
& {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,x \cr
& \therefore \text{Rate}\,\% \cr
& = \left( {\frac{{100 \times x}}{{x \times 7}}} \right)\% \cr
& = \frac{{100}}{7}\% \cr
& {\text{Now, sum}} = {\text{Rs}}{\text{. }}x \cr
& {\text{S}}{\text{.I}}. = {\text{Rs}}{\text{. }}3x \cr
& \text{Rate} = \frac{{100}}{7}\% \cr
& \therefore {\text{Total Time}} \cr
& = \left( {\frac{{100 \times 3x}}{{x \times \frac{{100}}{7}}}} \right){\text{years}} \cr
& = 21\,{\text{years}} \cr} $$
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$$\eqalign{
& {\text{Let sum}} = {\text{Rs}}{\text{. }}x \cr
& {\text{Then,}} \cr
& {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,x \cr
& \therefore \text{Rate}\,\% \cr
& = \left( {\frac{{100 \times x}}{{x \times 7}}} \right)\% \cr
& = \frac{{100}}{7}\% \cr
& {\text{Now, sum}} = {\text{Rs}}{\text{. }}x \cr
& {\text{S}}{\text{.I}}. = {\text{Rs}}{\text{. }}3x \cr
& \text{Rate} = \frac{{100}}{7}\% \cr
& \therefore {\text{Total Time}} \cr
& = \left( {\frac{{100 \times 3x}}{{x \times \frac{{100}}{7}}}} \right){\text{years}} \cr
& = 21\,{\text{years}} \cr} $$
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