Question

Mr Gupta borrowed ₹ 40,000 from a bank. at the end of 5years Mr Gupta had to pay to the bank ₹ 64,000 when was the rate of interest​

Answer 1

➤ Given :-

Principle :- ₹40000

Total Amount :- ₹64000

Time :- 5 years

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➤ To Find :-

The rate of interest applied to the loan.

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★ How to do :-

Here, we are given with the principle amount, the total amount paid at end of the time period and the time took to return the money back. We are asked to find the rate of interest that was applied to this loan. So, first we should find the simple interest by subtracting the total amount and the principle amount. The obtained answer will be the simple interest of this sum. Later, we can find the rate of interest by using the given formula below. So, let's solve!!

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➤ Solution :-

Simple Interest :-

${\tt \leadsto \underline{\boxed{\tt Total \: Amount - Principle}}}$

Substitute the given values.

${\tt \leadsto 64000 - 40000}$

Subtract the values to get the value of simple interest.

${\tt \leadsto \underline{24000}}$

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Now, let's find the rate of interest by using this formula.

Rate of interest :-

${\tt \leadsto \underline{\boxed{\tt \dfrac{SI \times 100}{P \times T}}}}$

Substitute the given values.

${\tt \leadsto \dfrac{24000 \times 100}{40000 \times 5}}$

Cancel the zeros in numerator and denominator.

${\tt \leadsto \dfrac{240 \cancel{00} \times 100}{400\cancel{00} \times 5} = \dfrac{240 \times 100}{400 \times 5}}$

Again cancel the zeros in numerator and denominator.

${\tt \leadsto \dfrac{240 \times 1 \cancel{00}}{4 \cancel{00} \times 5} = \dfrac{240 \times 1}{4 \times 5}}$

Multiply the numbers in numerator and denominator.

${\tt \leadsto \dfrac{240}{20}}$

Write the obtained fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{240}{20} = \pink{\underline{\boxed{\tt 12 \bf\%}}}}$

$\Huge\therefore$ The rate of interest of the sum is 12%.

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$\dashrightarrow$ Some related formulas :-

$\small\boxed{\begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Simple \: Interest :- \dfrac{P \times R \times T}{100}} \\ \\ \bigstar \: \sf{Principle :- \dfrac{SI \times 100}{R \times T}} \\ \\ \bigstar \: \sf{Time :- \dfrac{SI \times 100}{P \times R}}\end{array}}$