Citizens of Franistan pay numerically the same percent in income tax as they make in Rupees per week. (Example: If one makes 15 Rupees per week, he pays 15% in income tax.) What is the most a person can make after taxes are deducted in this country?
50%
To find the most a person can make after taxes are deducted in Franistan, we need to understand the relationship between income and taxes.
According to the given information, citizens of Franistan pay numerically the same percent in income tax as they make in Rupees per week. This means that the income tax rate is equal to the percentage of income earned.
Let's represent the income earned per week as "X" Rupees. The income tax rate will then be X%.
To calculate the amount of income that remains after taxes, we need to subtract the income tax paid from the total income earned. The income after taxes can be found using the following formula:
Income after taxes = Total income earned - Income tax paid
In this case, the income tax paid is calculated by multiplying the total income earned by the income tax rate as a decimal:
Income tax paid = X * (X/100)
Substituting this into the formula, we get:
Income after taxes = X - (X * (X/100))
Simplifying this equation gives us:
Income after taxes = X - X^2/100
To find the maximum income after taxes, we need to maximize the expression X - X^2/100.
This expression will be maximized when X is at its maximum value. In this case, the maximum value for X would be when it is equal to 100 (as the maximum income tax rate allowed is 100%).
Therefore, the most a person can make after taxes are deducted in Franistan is when they earn 100 Rupees per week.
To find the most a person can make after taxes are deducted in Franistan, you would need to understand the income tax system in the country.
According to the given information, citizens of Franistan pay numerically the same percent in income tax as they make in Rupees per week. For example, if someone makes 15 Rupees per week, they would pay 15% in income tax.
To solve this problem, we can assume a hypothetical income and calculate the after-tax amount until we find the maximum income.
Let's assume the weekly income as 'x' Rupees. According to the given information, the income tax paid would be 'x%' of x Rupees.
The after-tax income can be calculated as the difference between the total income and the income tax paid. Mathematically, it can be represented as:
After-tax income = x - (x * x/100) or x * (1 - x/100)
To find the maximum income after taxes, we can create an equation and solve for 'x':
x * (1 - x/100) = x_max
Taking the derivative of the equation with respect to 'x' and equating it to zero, we can find the maximum value of 'x':
1 - x/50 = 0
x/50 = 1
x = 50
Therefore, the maximum income a person can make after taxes are deducted in Franistan is 50 Rupees per week.