Question

Find the time:
i) $S.I. = $₹$663$, $P = $₹$2,000$, $R = $$10\dfrac{1}{5}\% $ per annum simple interest.
ii) $S.I. = $₹$1657.50$, $P = $₹$8,500$, $R = $$13\% $ per annum simple interest.

Answer 1

Hint: With the help of simple interest, we calculate the interest upon a given amount of loan, also known as principal amount. The formula for calculating Simple Interest is
$S.I. = \dfrac{{P \times R \times T}}{{100}}$ where $P$ is the principal amount, $R$ is the interest rate and $T$is the time period.
Moreover the final amount to be paid is the sum of the principal amount and simple interest.

Complete step by step solution:
We know that
$S.I. = \dfrac{{P \times R \times T}}{{100}}$
So the formula for time period will be
$ \Rightarrow T = \dfrac{{S.I. \times 100}}{{P \times R}}$
So for part (i) of the question:
We have
 $S.I. = $₹$663$
 $P = $₹$2,000$
$R = $$10\dfrac{1}{5}\% = \dfrac{{51}}{5}\% $. On using the obtained formula for time period, we will get
$T = \dfrac{{S.I. \times 100}}{{P \times R}}$$years$
On substituting the required values, we will get
$ \Rightarrow T = \dfrac{{663 \times 100}}{{2000 \times \dfrac{{51}}{5}}}$$years$
$ \Rightarrow T = \dfrac{{663 \times 100 \times 5}}{{2000 \times 51}}$$years$
On further calculating, we will get
$ \Rightarrow T = \dfrac{{331,500}}{{102,000}}$$years$
$ \Rightarrow T = \dfrac{{13}}{4}$$years$
On converting the obtained fraction into decimal, we will get
$ \Rightarrow T = 3.25$$years$
Hence, we get $3.25$$years$ at the time.
And, for part (ii) of the question:
We have
 $S.I. = $₹$1657.50$
 $P = $₹$8,500$
$R = $$13\% $. On using the obtained formula for time period, we will get
$T = \dfrac{{S.I. \times 100}}{{P \times R}}$$years$
On substituting the required values, we will get
$ \Rightarrow T = \dfrac{{1657.50 \times 100}}{{8500 \times 13}}$$years$
On further calculating, we will get
$ \Rightarrow T = \dfrac{{165750}}{{110500}}$$years$
$ \Rightarrow T = \dfrac{3}{2}$$years$
On converting the obtained fraction into decimal, we will get
$ \Rightarrow T = 1.5$$years$

Hence, we get $1.5$$years$ at the time.

Note:
In the questions of Simple Interest, the time period is sometimes given in terms of months and not years. For solving such questions, we will then divide the given month by $12$ so as to convert it into years. It must be noted that the time period must only be in years so as to substitute in the formulae.