Question

an amount doubles it in 5yrs with simple interest. What is the rate of interest per annum..​

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Amount is double of principle
• Time = 5 years

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Rate = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

• let the principle be x

$\sf{\red{\boxed{\bold{Simple\: Interest = \dfrac{ P\times R \times T}{100}}}}}$

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$\sf: \implies{\bold{Simple\: Interest = \dfrac{ x \times R \times 5}{100}}}$

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$\sf: \implies{\bold{Simple\: Interest = \dfrac{ Rx}{20 }}}$

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• Amount = 2 × principle = 2x

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$\sf{\red{\boxed{\bold{Amount = Principle + Interest}}}}$

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$\sf: \implies{\bold{2x = x + \dfrac{ Rx}{20}}}$

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$\sf: \implies{\bold{2x = \dfrac{ 20x + Rx}{20}}}$

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$\sf: \implies{\bold{2x \times 20 = 20x + Rx}}$

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$\sf: \implies{\bold{40x = 20x + Rx}}$

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$\sf: \implies{\bold{Rx = 40x - 20x }}$

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$\sf: \implies{\bold{Rx = 20x }}$

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$\sf: \implies{\bold{R = 20\%}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Principle will double in 5 years at 20% per annum .