Question

At what rate percent per year will a sum
1
double itself in 6 years?​

Answer 1

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

• Amount = 2 × Principle
• Time = 6 years

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

• Rate = ??

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

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Let the principle be x

Therefore Amount = 2x

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

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Interest = 2x - x

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Interest = x

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

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$\sf: \implies\: {\bold{ x = \dfrac{x \times R \times 6}{100}}}$

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$\sf: \implies\: {\bold{ x= \dfrac{x \times R\times 3}{50}}}$

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$\sf: \implies\: {\bold{ R = \dfrac{x\times 50}{x \times 3}}}$

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$\sf: \implies\: {\bold{ R = \dfrac{50}{3}}}$

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$\sf: \implies\: {\bold{ R = 16 \dfrac{2}{3}\%}}$

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

• At the rate of 50/3 % Amount will be double of principle in 6 years

Answer 2

$\huge\mathbb{Answer:-}$

According to Statement:-

Amount = 2 × Principal

Time = 6 yrs

Rate = ?

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Let principle = x

$\sf \therefore Amount = 2x$

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As, We know that,

Interest = Amount - Principle

$\sf \therefore Interest = 2x - x$

$\boxed{\sf Interest = x}$

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Now, we know that,

$\sf Interest =\dfrac{Principle \times Rate \times Time}{100}$

$\sf x = \dfrac{x \times Rate \times 6}{100}$

$\sf x= \dfrac{x \times Rate \times 3}{50}$

$\sf Rate = \dfrac{x\times 50}{x \times 3}$⠀

$\sf Rate = \dfrac{50}{3}$

$\boxed{\sf Rate = \dfrac{50}{3}\%}$

$\sf \color{fuchsia} Therefore, \: rate \: is \: \dfrac{50}{3}\%$