Question

If a certain sum becomes 2/5th of the amount in 5years,then find the rate of interest.

Answer 1

Given:-

•Sum of money becomes $\dfrac{2}{5}$.

•Time taken 5years.

To Find:-

•Find the rate of interest.

Solution:-

Let assume the principal be P and time = 5years.

From the question,

$\: \: \sf \: p = \frac{2}{5} a \\ \\ \: \: \sf \: a = \frac{5}{2} p$

As we know,

$\: \: \sf \: simple \: interest = amount - principal$

Now substitute the values

$\: \: \sf \: simple \: interest = \frac{5}{2} p - p \\ \\ \: \: \sf \: simple \: interest = \frac{3}{2} p$

Hence,Simple Interest is $\dfrac{3}{2}$P.

As we know,

$\: \: \sf \: rate = \frac{simple \: interest \times 100}{principal \times time}$

Now substitute the values

$\: \: \sf \: rate = \frac{ \frac{3}{2}p \times 100 }{p \times 5} \\ \\ \: \: \sf \: rate = 30 \: percent$

Hence,Rate of interest is 30%.

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