If a citizen has paid taxes equal to (p + 0, 25%) of its income overall what was income

Question

In the state of the income tax was ill-treated and 28 000 p% on the first and then go to c (p + 2)% for
part of the income exceeding 28 000 c. If a citizen has paid taxes equal to (p + 0, 25%) of its income
Overall, what was this income

Answer 1

Let P (pay) be the income, where P>28000, then tax on the first 28000 will be 28000p/100=280p.

The remaining part of the income is P-28000 and is taxed at c%, so the tax for this is (P-28000)c/100.

Total tax is 280p+(P-28000)c/100=280p+Pc/100-280c.

We are given the overall tax as (p+0.25)%=(p+0.25)/100.

So (p+0.25)P/100=280p+Pc/100-280c,

(p+0.25)P=28000p+Pc-28000c,

pP+0.25P-Pc=28000(p-c),

P=28000(p-c)/(p-c+0.25), or 28000/(1+0.25/(p-c)) or 28000/(1-0.25/(c-p)).

Note that p<c because P has to be greater than 28000. The denominator has to be less than 1 for P to be greater than 28000.

EXAMPLE

p=10% and c=12.5%, P=28000/(1-0.25/2.5)=28000/0.9=31111 approx.

Tax on first 28000 is 2800; remaining pay is 3111, taxed at 12.5%=389 (approx). Total tax is 2800+389=3189.

(p+0.25)%=10.25% and 10.25% of 31111=3189 approx.