Question

Manish borrowed $₹1000$ from a friend for a simple interest rate of $6\%$ per annum. He returned his friend ₹ 1300. How long did Manish take to return the money?

• A. $2$ years
• B. $3$ years
• C. $5$ years
• D. $6$ years

Answer 1

The correct option is C $5$ years

Here, principal (starting amount) $=₹1000$
Total amount $=₹1300$

We get the total amount by adding the interest to the principal.
$\because$ Principal + Simple Interest = Total Amount
$\Rightarrow$ Simple Interest = Amount - Principal
$\Rightarrow \text{Simple Interest =}₹1300-₹1000$
$\Rightarrow \text{Simple Interest =}₹300\dots \left(i\right)$

Also, $\text{Simple Interest}=\frac{PRT}{100}\dots \left(ii\right)$
where, P = Principal, R = Rate of interest (expressed in $\%$ per annum) and T = time period (in years)

From $\left(i\right)$ and $\left(ii\right),$ we get
$300=\frac{PRT}{100}$
$\Rightarrow 300=\frac{1000\times 6\times T}{100}$
On simplifying, we get
$300=10\times 6\times T$
$\Rightarrow 300=60\times T$

Dividing both the sides by $60,$ we get
$\frac{300}{60}=T$
Simplify and cancel the common factors, we get
$T=\frac{5\times 60}{60}$
$\Rightarrow T=5$ years

Hence, Manish returned the money after 5 years.