[5%] If a sum of money trebles itself in 40 years,what is the rate of interest?

If a sum of money trebles itself in 40 years,what is the rate of interest?

None of these

Explanation:

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Solution 1

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Let the sum of money be Rs.x

After 40 years, this becomes 3x

Simple Interest = $\left(3x - x\right)$ = 2x

$\text{Simple Interest = }\dfrac{\text{PRT}}{100}$

$2x =\dfrac{x \times \text{R} \times 40}{100}$

$2 =\dfrac{\text{R} \times 40}{100}$

$200 =40\text{R}$

$\text{R} = 5\%$

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Solution 2

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If a sum of money becomes n times in T years at simple interest, then the rate of interest per annum can be given be

$\text{R = }\dfrac{100(\text{n}-1)}{\text{T}}\%$

n = 3

T = 40

$\text{R = }\dfrac{100(\text{n}-1)}{\text{T}} = \dfrac{100(3-1)}{40} = \dfrac{100 \times 2}{40} = \dfrac{100}{20} = 5\%$

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