Question

A country follows a progressive taxation system under which the income tax rates applicable varies for different slabs of income. Total tax is computed by calculating the tax for each slab and adding them up. The rates applicable are as follows :
% Requires: \usepackage{graphicx} \begin{table}[h] \centering \begin{tabular}{|c|c|} \hline Annual income & Tax rate
\hline 0 - 50,000 & 0\%
\hline 50,001 - 60,000 & 10\%
\hline 60,001 - 1,50,000 & 20\%
\hline > 1,50,000 & 30\%
\hline \end{tabular} \caption{Tax Rate Table Based on Annual Income} \label{tab:tax_rate} \end{table} If annual income is ₹ $1{,}70{,}000$, what is the total tax payable?

• A. ₹ 51{,}000
• B. ₹ 17{,}000
• C. ₹ 34{,}000
• D. ₹ 25{,}000

Hint:

In a progressive system, never apply one rate to the whole income. Break the income across slabs, compute each slab's tax, then add. A quick check: the top-bracket portion here is only ₹ 20{,}000, so at $30\%$ that part can contribute at most ₹ 6{,}000.

Answer 1

The Correct Option is D

Step 1 (Write the income as a sum over slabs).
\[ 1{,}70{,}000 =\underbrace{50{,}000}_{0\%} +\underbrace{10{,}000}_{10\%} +\underbrace{90{,}000}_{20\%} +\underbrace{20{,}000}_{30\%}. \] \medskip Step 2 (Compute tax contributed by each slab).
\begin{align*} \text{Tax on first }50{,}000 &: 0\%\Rightarrow ₹ 0,
\text{Tax on next }10{,}000 &: 10\%\Rightarrow 0.10\times 10{,}000=₹ 1{,}000,
\text{Tax on next }90{,}000 &: 20\%\Rightarrow 0.20\times 90{,}000=₹ 18{,}000,
\text{Tax on last }20{,}000 &: 30\%\Rightarrow 0.30\times 20{,}000=₹ 6{,}000. \end{align*} \medskip Step 3 (Add the slab-wise amounts).
\[ \text{Total tax}=₹(0+1{,}000+18{,}000+6{,}000)=\boxed{₹ 25{,}000}. \] \medskip (Why not the other options?)
₹ 34{,}000 and ₹ 51{,}000 come from incorrectly applying a single high rate to the full income; ₹ 17{,}000 ignores the $30\%$ slab.