True discount whispers the secret price: 189 rupees! But time and interest levy their tax, pushing the bill's true worth up to 1764, a tidy sum! Let buyers beware – discounts hide the final pay. So, The correct answer is B. Rs. 1764.
Here's how to find the amount of the bill:
Present Value (PV) Formula: We know the true discount (TD) and the interest rate (R), but we need to find the present value (PV) of the bill. The formula for calculating PV is:
PV = TD / (1 + R * T)
where:
- TD = True discount = Rs. 189
- R = Interest rate = 16% (converted to decimal: 0.16)
- T = Time = 9 months (converted to years: 9/12 = 0.75)
2. Calculating PV: Plugging the values into the formula:
PV = 189 / (1 + 0.16 * 0.75) ≈ Rs. 1575
3. Amount of Bill: The amount of the bill is the sum of the present value and the true discount:
Amount = PV + TD = Rs. 1575 + Rs. 189 = Rs. 1764
Therefore, the amount of the bill is Rs. 1764.
Remember, the other options are incorrect:
- Option A (Rs. 1386) is too low because it doesn't account for the interest due on the bill.
- Option C (Rs. 1575) is the present value, not the amount of the bill.
- Option D (Rs. 2268) is too high and likely includes errors in calculation.
Therefore, The correct answer is B. Rs. 1764.