Question

At simple interest a sum becomes 7 /4 of itself in 5 years. The rate of interest is

Answer 1

Given:-

• At simple interest, a sum becomes 7/4 of itself in 5 years.

To find:-

• The rate of interest is?

Formulas to be used:-

$\boxed{\bold{S.I. = \frac{PRT}{100} }}\\\\\boxed{\bold{A = P + S.I. }}$

Solution:-

Let,

• "P" → represents the sum of money.
• "R" → represents the rate of interest.
• "T" → represents the no. of years.

As given in the question, Amount, A = $\frac{7}{4} \:of\:principal = \frac{7}{4} \times P$

T = 5 years

∴ S.I. = A - P = $\frac{7P}{4} - P = \frac{3P}{4}$

• $\textsf{Now, on substituting the value of P, T & S.I. in the formula of S.I., we get}$

$\frac{3P}{4} = \frac{P \times R \times 5}{100}$

$\implies \frac{3}{4} = \frac{ R \times 5}{100}$

$\implies \frac{3}{4} = \frac{ R \times 1}{20}$

$\implies 3 = \frac{ R \times 1}{5}$

$\implies R = 3 \times 5$

$\implies \bold{R = 15\%}$

Thus, rate of interest is → 15%.

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