Question

at what rate of interest ,would Rs.1800 amount to Rs.2500 in 2 years ?

Answer 1

➤ Given :-

Principle :- ₹1800

Total Amount :- ₹2500

Time :- 2 years

$\:$

➤ To Find :-

The rate of interest of this loan or investment.

$\:$

★ How to do :-

Here, we are given with the principle amount, the total amount and the time taken to return back the money. We are asked to find the rate of interest applied to this loan or investment. We have an appropriate formula to calculate the rate of interest which will be used here. But, for finding the rate of interest in that method, we are needed with the simple interest which isn't given here. So, first we should find the simple interest by subtracting the total amount and the principle amount. Later, we can find the rate of interest in percent form by the use of given formula. So, let's solve!!

$\:$

➤ Solution :-

Simple Interest :-

${\sf \longrightarrow \underline{\boxed{\sf Total \: Amount - Principle}}}$

Substitute the given values.

${\tt \leadsto 2500 - 1800}$

Subtract the values to get the interest amount.

${\tt \leadsto Rs \: \: 700}$

$\:$

Now, let's solve for the rate of interest.

Rate of interest :-

${\sf \longrightarrow \underline{\boxed{\sf \dfrac{SI \times 100}{P \times T}}}}$

Substitute the given values.

${\tt \leadsto \dfrac{700 \times 100}{1800 \times 2}}$

Cancel the zeros in numerator and denominator.

${\tt \leadsto \dfrac{7 \cancel{00} \times 100}{18 \cancel{00} \times 2} = \dfrac{7 \times 100}{18 \times 2}}$

Again write the numerator and denominator in lowest form.

${\tt \leadsto \dfrac{7 \times \cancel{100}}{\cancel{18} \times 2} = \dfrac{7 \times 50}{9 \times 2}}$

Now, multiply the remaining numbers.

${\tt \leadsto \dfrac{350}{18}}$

Write the obtained fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{350}{18} = 19.44 \bf\%}$

$\:$

${\red{\underline{\boxed{\bf So, \: the \: rate \: of \: interest \: is \: 19.44 \%.}}}}$