Question

If Rs.250 amounts to Rs.285 in 2 years, find the rate percent per annum.

Answer 1

Hint: In this question, we are given the principal amount the amount after added Rs. interest, and the time period. We need to find the rate of interest per annum. For this, we will first calculate the simple interest by subtracting the principal amount from the amount after added interest. Then we will find the rate of interest using the formula $SI=\dfrac{P\times R\times T}{100}$ where SI is the simple interest, P is the principal amount, R is the rate of interest per annum and T is the time period.

Complete step by step answer:
Here we are given the principal amount as Rs.250. Therefore, P = Rs.250. We are also given the amount after added interest as Rs.285. Therefore, A = Rs.285. The time period is given as 2 years. Therefore, T = 2 years.
Let us suppose that the rate of interest per annum (in percentage) is r.
Let us first calculate the simple interest. We know that simple interest is the difference between the amount A and principal amount P. Therefore, Simple interest = A - P.
$\Rightarrow Rs.285-Rs.250=Rs.35$.
So the simple interest is Rs.35, or we can say SI = Rs.35.
Now we know from the formula of simple interest that, $SI=\dfrac{P\times R\times T}{100}$ where P is the principal amount, R is the rate of interest, T is the period and SI is the simple interest. So putting in all the values we get, $35=\dfrac{250\times r\times 2}{100}$.
Multiplying 250 by 2 gives us 500 so we have $35=\dfrac{500}{100}r\Rightarrow 35=5r$.
Dividing both sides by 5, we get $\dfrac{35}{5}=\dfrac{5r}{5}$.
Simplifying we get, $7=r$.
Since units of r are in percentage so the rate of interest is 7% per annum.

Note:
Students should note that we have used percentage because, through the formula of simple interest, the rate of interest per annum is calculated in percentage only (100 is divided in the formula). Take care of signs while solving this sum.