The income tax rate is increased by 24%, which causes a person's net…

Concept: If a fixed gross income is taxed at rate r, net (post-tax) income equals Income × (1 − r). When the rate rises by a known percentage while gross income stays fixed, the resulting fractional drop in net income can be written as one linear equation in r — solving that equation gives the original rate directly.

1. Let the original tax rate be r (as a fraction of income) and let gross income be I. The original net income is I(1 − r).

2. The rate rises by 24%, so the new rate is 1.24r, and the new net income is I(1 − 1.24r).

3. The net income falls by 1% of the original net income, so I(1 − r) − I(1 − 1.24r) = 0.01 × I(1 − r).

4. The left side simplifies to I(1.24r − r) = I(0.24r), so 0.24r = 0.01(1 − r).

5. Expand and collect the r terms: 0.24r + 0.01r = 0.01, i.e. 0.25r = 0.01.

6. Solve: r = 0.01 ÷ 0.25 = 0.04, i.e. 4%.

Cross-check: at r = 4%, original net income is 96% of gross income. The raised rate is 1.24 × 4% = 4.96%, so the new net income is 95.04% of gross income. The fall is 0.96 percentage points of gross income, which is 0.96 ÷ 96 = 1% of the original net income — exactly matching the given condition.

So the original rate of tax is 4%.