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In a certain community, property is assessed at 60% of its appraised value and taxed annually at the rate of Tk. 4.00 per Tk. 100 of assessed value. If a taxpayer is assessed Tk. 240 per quarter in property taxes, what is the appraised value of the property?
Total tax of assessed = ( 240×4) Tk. = 960Tk.
Tk. 4 is tax of Tk. 100
Tk.960 is tax of Tk. ( 100/4 ×960) = 24000 Tk.
So, 60% of x = 24000Tk.
60x×x /100 = 24000
x = 2400000/60 = 40000 Tk.
To determine the appraised value of the property, we need to follow these steps:
1. **Determine the total annual property tax:**
The taxpayer is assessed $240 per quarter. There are 4 quarters in a year, so the total annual property tax is:
\[
240 \text{ (per quarter)} \times 4 \text{ (quarters)} = 960 \text{ (annual property tax)}
\]
2. **Calculate the assessed value of the property:**
The tax rate is $4.00 per $100 of assessed value. Therefore, to find the assessed value that corresponds to an annual tax of $960:
\[
\text{Tax rate} = \frac{4}{100} = 0.04 \text{ (per dollar of assessed value)}
\]
Let \( A \) be the assessed value. We can write:
\[
0.04 \times A = 960
\]
Solving for \( A \):
\[
A = \frac{960}{0.04} = 24,000
\]
3. **Determine the appraised value:**
The assessed value is 60% of the appraised value. Let \( P \) be the appraised value. Therefore:
\[
\text{Assessed value} = 0.60 \times P
\]
We already found the assessed value to be $24,000. So:
\[
24,000 = 0.60 \times P
\]
Solving for \( P \):
\[
P = \frac{24,000}{0.60} = 40,000
\]
Thus, the appraised value of the property is \( \boxed{40,000} \).
