What principal would amount to ₹21,420 in 2 years at the rate of 9.5% p.a. simple interest?

The correct option is ₹18,000.

To find the principal amount that will yield a total amount of ₹21,420 in 2 years at a simple interest rate of 9.5% per annum, we can use the simple interest formulas.

Let:
- Principal amount = $P$
- Rate of interest per annum ($R$) = 9.5%
- Time period ($T$) = 2 years
- Total Amount ($A$) = ₹21,420

The formula for Simple Interest ($\mathrm{SI}$) is given by:

$\mathrm{SI}=\frac{P\times R\times T}{100}$

The total Amount ($A$) is the sum of the Principal ($P$) and the Simple Interest ($\mathrm{SI}$):

$A=P+\mathrm{SI}$

By substituting the simple interest formula into the amount equation, we get:

$A=P+\frac{P\times R\times T}{100}$

Taking $P$ common on the right-hand side:

$A=P\left(1+\frac{R\times T}{100}\right)$

Now, let's substitute the given values into the equation:

$\mathrm{21,420}=P\left(1+\frac{9.5\times 2}{100}\right)$

First, calculate the product inside the parenthesis:

$9.5\times 2=19$

Now, substitute this value back into the equation:

$\mathrm{21,420}=P\left(1+\frac{19}{100}\right)$

$\mathrm{21,420}=P\left(1+0.19\right)$

$\mathrm{21,420}=P\times 1.19$

Solve for $P$ by dividing both sides by 1.19:

$P=\frac{\mathrm{21,420}}{1.19}$

To simplify the division, we can multiply the numerator and the denominator by 100:

$P=\frac{\mathrm{2,142,000}}{119}$

Now, performing the division:

$\mathrm{2,142,000}÷119=\mathrm{18,000}$

Therefore, the principal amount is ₹18,000.