Question
Consider the following statements
If a sum of money is lent at simple interest, then the
I - money gets doubled in 5 years if the rate of interest is $$16\frac{2}{3}$$ %
II - money gets doubled in 5 years if the rate of interest is 20%.
III - money becomes four times in 10 years if it gets doubled in 5 years.
If a sum of money is lent at simple interest, then the
I - money gets doubled in 5 years if the rate of interest is $$16\frac{2}{3}$$ %
II - money gets doubled in 5 years if the rate of interest is 20%.
III - money becomes four times in 10 years if it gets doubled in 5 years.
Answer: Option B
$$\eqalign{
& {\text{Let sum be x}}{\text{.}} \cr
& {\text{Then,}} \cr
& {\text{S}}{\text{.I}}{\text{.}} = x \cr
& {\text{I - Time}} \cr
& = \frac{{100 \times x}}{{x \times \frac{{50}}{3}}} \cr
& = 6\,{\text{years(false)}} \cr
& {\text{II}} - {\text{Time}} \cr
& = \frac{{100 \times x}}{{x \times 20}} \cr
& = 5\,{\text{years(True)}} \cr
& {\text{III}} - {\text{Suppose sum}} = x. \cr
& {\text{Then, S}}{\text{.I}}{\text{. }} = x \cr
& {\text{Time }} = {\text{5 }}{\text{years}}{\text{.}} \cr
& {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 5}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = 20\% . \cr
& {\text{Now, sum}} = x,\,{\text{S}}{\text{.I}}{\text{.}} = 3x\,{\text{and}}\,{\text{Rate}} = 20\% \cr & \therefore {\text{Time}} = \left( {\frac{{100 \times 3x}}{{x \times 20}}} \right){\text{years}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15\,{\text{years}}(\text{false}) \cr
& {\text{So, B alone is correct}}{\text{.}} \cr} $$
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$$\eqalign{
& {\text{Let sum be x}}{\text{.}} \cr
& {\text{Then,}} \cr
& {\text{S}}{\text{.I}}{\text{.}} = x \cr
& {\text{I - Time}} \cr
& = \frac{{100 \times x}}{{x \times \frac{{50}}{3}}} \cr
& = 6\,{\text{years(false)}} \cr
& {\text{II}} - {\text{Time}} \cr
& = \frac{{100 \times x}}{{x \times 20}} \cr
& = 5\,{\text{years(True)}} \cr
& {\text{III}} - {\text{Suppose sum}} = x. \cr
& {\text{Then, S}}{\text{.I}}{\text{. }} = x \cr
& {\text{Time }} = {\text{5 }}{\text{years}}{\text{.}} \cr
& {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 5}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = 20\% . \cr
& {\text{Now, sum}} = x,\,{\text{S}}{\text{.I}}{\text{.}} = 3x\,{\text{and}}\,{\text{Rate}} = 20\% \cr & \therefore {\text{Time}} = \left( {\frac{{100 \times 3x}}{{x \times 20}}} \right){\text{years}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15\,{\text{years}}(\text{false}) \cr
& {\text{So, B alone is correct}}{\text{.}} \cr} $$
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