A bill drawn for Rs. 2700 was discounted in the bank for Rs. 2655. If the rate of discount was 5% p. a., find the time for which the bill was drawn.

Solution

Given:

• Face value (FV) of the bill = Rs. 2700
• Present value (PV) received after discounting = Rs. 2655
• Rate of discount (r) = 5% per annum
• Discount (D) = FV − PV = Rs. 2700 − Rs. 2655 = Rs. 45

Step 1: Understand the formula for simple discounting The formula for simple discounting is: $$D=\frac{FV\times r\times t}{100}$$ where:

• $D$ = Discount amount
• $FV$ = Face value of the bill
• $r$ = Rate of discount per annum
• $t$ = Time period (in years)

Step 2: Substitute the known values into the formula $$45=\frac{2700\times 5\times t}{100}$$

Step 3: Simplify the equation $$45=\frac{13500\times t}{100}$$ $$45=135\times t$$

Step 4: Solve for $t$ $$t=\frac{45}{135}$$ $$t=\frac{1}{3}\text{ years}$$

Step 5: Convert the time into months Since 1 year = 12 months, $$t=\frac{1}{3}\times 12=4\text{ months}$$

Final Answer: The bill was drawn for 4 months.