1919\frac{1}{9} of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -" /> 1919\frac{1}{9} of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -" /> 1919\frac{1}{9} of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -" />

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Simple interest on a certain sum at a certain annual rate of interest is $\frac{1}{9}$ $\frac{1}{9}$ of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -

1 $3 \frac{1}{3}$ $3\frac{1}{3}$ %
25%
3 $6 \frac{2}{3}$ $6\frac{2}{3}$ %
410%

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let sum = x \\ Then, \\ S .I . = \frac{x}{9} . \\ Let rate = R % and \\ time = R years . \\ ∴ (\frac{x \times R \times R}{100}) = \frac{x}{9} \\ \Rightarrow R^{2} = \frac{100}{9} \\ \Rightarrow R = \frac{10}{3} = 3 \frac{1}{3} \\ Hence, rate = 3 \frac{1}{3} % \end{aligned}

$\eqalign{ & {\text{Let sum}} = x \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{x}{9}. \cr & {\text{Let rate}} = {\text{R}}\% \,{\text{and}} \cr & {\text{time}} = {\text{R}}\,{\text{years}}{\text{.}} \cr & \therefore \left( {\frac{{x \times {\text{R}} \times {\text{R}}}}{{100}}} \right) = \frac{x}{9} \cr & \Rightarrow {{\text{R}}^2} = \frac{{100}}{9} \cr & \Rightarrow {\text{R}} = \frac{{10}}{3} = 3\frac{1}{3} \cr & {\text{Hence, rate}} = 3\frac{1}{3}\% \cr}$

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of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -", "text": "Simple interest on a certain sum at a certain annual rate of interest is

\frac{1}{9}

$\frac{1}{9}$ of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Let sum = x \\ Then, \\ S .I . = \frac{x}{9} . \\ Let rate = R % and \\ time = R years . \\ ∴ (\frac{x \times R \times R}{100}) = \frac{x}{9} \\ \Rightarrow R^{2} = \frac{100}{9} \\ \Rightarrow R = \frac{10}{3} = 3 \frac{1}{3} \\ Hence, rate = 3 \frac{1}{3} % \end{aligned}

$\eqalign{ & {\text{Let sum}} = x \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{x}{9}. \cr & {\text{Let rate}} = {\text{R}}\% \,{\text{and}} \cr & {\text{time}} = {\text{R}}\,{\text{years}}{\text{.}} \cr & \therefore \left( {\frac{{x \times {\text{R}} \times {\text{R}}}}{{100}}} \right) = \frac{x}{9} \cr & \Rightarrow {{\text{R}}^2} = \frac{{100}}{9} \cr & \Rightarrow {\text{R}} = \frac{{10}}{3} = 3\frac{1}{3} \cr & {\text{Hence, rate}} = 3\frac{1}{3}\% \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Let sum = x \\ Then, \\ S .I . = \frac{x}{9} . \\ Let rate = R % and \\ time = R years . \\ ∴ (\frac{x \times R \times R}{100}) = \frac{x}{9} \\ \Rightarrow R^{2} = \frac{100}{9} \\ \Rightarrow R = \frac{10}{3} = 3 \frac{1}{3} \\ Hence, rate = 3 \frac{1}{3} % \end{aligned}

$\eqalign{ & {\text{Let sum}} = x \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{x}{9}. \cr & {\text{Let rate}} = {\text{R}}\% \,{\text{and}} \cr & {\text{time}} = {\text{R}}\,{\text{years}}{\text{.}} \cr & \therefore \left( {\frac{{x \times {\text{R}} \times {\text{R}}}}{{100}}} \right) = \frac{x}{9} \cr & \Rightarrow {{\text{R}}^2} = \frac{{100}}{9} \cr & \Rightarrow {\text{R}} = \frac{{10}}{3} = 3\frac{1}{3} \cr & {\text{Hence, rate}} = 3\frac{1}{3}\% \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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