Ravi’s salary is increased by 20%. On the increased salary, the tax rate is 10% higher. The percentage increase in tax liability is:
Correct Answer :
22%
Solution :
The correct option is 22%.
To understand why this is the correct answer, we look at the interpretation of the problem where the tax rate is increased only on the incremental (increased) portion of the salary. Let us break down the steps using this logical derivation:
First, we assume convenient initial values to simplify the percentage calculations.
Let Ravi's initial salary be:
Let the initial tax rate on this base salary be:
Therefore, the initial tax liability is:
Now, we find the increment in Ravi's salary. Since the salary is increased by 20%, the increased portion (increment) is:
The problem states that on this increased salary portion, the tax rate is 10% higher than the initial tax rate.
Thus, the tax rate applied to the incremental salary is:
Now, we calculate the tax liability on the incremental salary of 20:
Next, we sum the initial tax liability and the tax on the increment to get the new total tax liability:
Finally, we calculate the percentage increase in tax liability:
Substituting the calculated values:
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