In what time will ₹3,720 amount to ₹5,282.4 at 12% simple interest per annum?

The correct option is 3$\frac{1}{2}$ years.

Let's find the time step-by-step using the formulas for simple interest.

1. Identify the given values:
Principal ($P$) = ₹3,720
Amount ($A$) = ₹5,282.4
Rate of Interest ($R$) = 12% per annum

2. Calculate the Simple Interest (SI):
The simple interest earned is the difference between the total amount and the principal:
$\mathrm{SI}=A-P$

$\mathrm{SI}=\mathrm{5,282.4}-\mathrm{3,720}$

$\mathrm{SI}=₹\mathrm{1,562.4}$

3. Use the Simple Interest formula to find the Time (T):
The formula for simple interest is:
$\mathrm{SI}=\frac{P\times R\times T}{100}$

Rearranging the formula to solve for time ($T$):
$T=\frac{\mathrm{SI}\times 100}{P\times R}$

Substitute the values into the equation:
$T=\frac{\mathrm{1,562.4}\times 100}{\mathrm{3,720}\times 12}$

$T=\frac{\mathrm{156,240}}{\mathrm{44,640}}$

4. Simplify the fraction:
Divide both numerator and denominator by 10:
$T=\frac{\mathrm{15,624}}{\mathrm{4,464}}$

Divide both by their greatest common divisor, 4,464:
$T=3.5\text{years}$

Expressing the decimal as a mixed fraction:
$T=3\frac{1}{2}\text{years}$

Therefore, the time required is 3$\frac{1}{2}$ years.