Question

A sum of money becomes 5/4 of itself in 5 years at a certain rate of simple interest. Find the rate of interest?

Answer 1

Let :

• Initial sum of money ( principal) = x

Given :

• Amount (A) = (5/4) of initial sum of money
• Time (t) = 5 years

To find :

Rate of simple interest

Formula used :

• A = P + I
• I = Prt

Solution :

Amount = (5/4)of principal

A = (5/4) x

Now , Interest (I) = Amount - Principal

I = (5/4)x - x

I = (1/4)x

Put all value in, I = Prt

$\sf \implies \: \dfrac{1}{4}x \: = \: x \times \bigg \{ \dfrac{r\%}{100} \bigg\} \times 5 \\ \\ \sf \implies \:\dfrac{r\%}{100} \: = \: \dfrac{1}{4} x \: \times \dfrac{1}{5x} \\ \\ \sf \implies \: r\% \: = \: \dfrac{100}{20} \\ \\ \sf \implies \: r\% \: = \bold{5\%}$

ANSWER :

Rate = 5% per annum

Answer 2

Answer:- 5% per annum

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Explanation:-

According to Question, we have to find the Rate of Simple Interest!

So,

Amount=$\frac{5}{4}$of Principal

Time=5 years

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Let the Value of Principal be x !

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Formula that are going to be used in the Question are:-

• Amount = Principal + Interest

• Interest = Principal × Rate × Time

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Solution :-

Amount = $\frac{5}{4}$ of x

Interest = Amount - Principal

Interest = $\frac{5}{4}$ of x - x

Interest = $\frac{1}{4}$x

Formula For Interest is :

Interest = Principal × Rate × Time

$\frac{1}{4}$x = x × { r% / 100 } × 5

( r% / 100 )=$\frac{1}{4}$x × $\frac{1}{5x}$

r% = $\frac{100}{20}$

r% = 5%

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