What annual instalment will discharge a debt of ₹10,192 due in 3 years at 10% simple interest?

The correct option is ₹3,088.

Step-by-Step Explanation:

Let the annual instalment paid at the end of each year be ₹$x$.

When a debt is discharged in instalments, each instalment (except the last one) accumulates simple interest up to the final due date:

1. 1st Instalment (paid at the end of Year 1):
This payment remains with the lender for the remaining 2 years until the due date.
$\text{Value at maturity}=x+\left(\frac{x\times 10\times 2}{100}\right)=x+0.20x=1.20x$

2. 2nd Instalment (paid at the end of Year 2):
This payment remains with the lender for the remaining 1 year.
$\text{Value at maturity}=x+\left(\frac{x\times 10\times 1}{100}\right)=x+0.10x=1.10x$

3. 3rd Instalment (paid at the end of Year 3):
This is paid on the due date itself, so it earns no interest.
$\text{Value at maturity}=x$

Setting up the equation:

The sum of the maturity values of all 3 instalments must discharge the total debt of ₹10,192:

$1.20x+1.10x+x=10192$

$3.30x=10192$

$x=\frac{10192}{3.30}=3088.48$

Rounding to the nearest whole integer, the annual instalment is ₹3,088.