What is the face value of a bill if the bankers' discount is Rs. 500, the rate is 10% per annum, and the time is 6 months?

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Q: What is the face value of a bill if the bankers' discount is Rs. 500, the rate is 10% per annum, and the time is 6 months?

Solution: Face Value = BD / (Rate × Time) = 500 / (10 × 0.5) = Rs. 5000.

Steps: 8

Step 1: Identify the given values. The bankers' discount (BD) is Rs. 500, the rate is 10% per annum, and the time is 6 months.
Step 2: Convert the rate from percentage to decimal. 10% as a decimal is 0.10.
Step 3: Convert the time from months to years. 6 months is equal to 0.5 years.
Step 4: Use the formula for face value: Face Value = BD / (Rate × Time).
Step 5: Substitute the values into the formula: Face Value = 500 / (0.10 × 0.5).
Step 6: Calculate the denominator: 0.10 × 0.5 = 0.05.
Step 7: Divide the bankers' discount by the result from Step 6: Face Value = 500 / 0.05.
Step 8: Calculate the final result: Face Value = Rs. 5000.