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Earlier, the tax laws of a country required one of pay flat 20% of one

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Earlier, the tax laws of a country required one of pay flat 20% of one [#permalink]

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New post 25 Nov 2017, 11:18
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Question Stats:

63% (01:18) correct 38% (01:58) wrong based on 16 sessions

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Earlier, the tax laws of a country required one of pay flat 20% of one's income. Recently, the concept of progressive tax was implemented and one now needs to pay 30% income tax on the part of one's income above $40000. Jack paid the same amount of tax this year although he earned $10000 more than he did the previous year. What was Jack's income this year?

A. $70000
B. $80000
C. $90000
D. $100000
E. $120000

Source: Experts Global
[Reveal] Spoiler: OA

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Earlier, the tax laws of a country required one of pay flat 20% of one [#permalink]

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pushpitkc wrote:
Earlier, the tax laws of a country required one of pay flat 20% of one's income. Recently, the concept of progressive tax was implemented and one now needs to pay 30% income tax on the part of one's income above $40000. Jack paid the same amount of tax this year although he earned $10000 more than he did the previous year. What was Jack's income this year?

A. $70000
B. $80000
C. $90000
D. $100000
E. $120000

Source: Experts Global


Last year Jack paid taxes at a flat rate of 20 percent of income.

This year he paid exactly the same dollar amount in taxes, at a rate of 30 percent for income greater than $40,000, AND he earned $10,000 more this year.

Let x = this year's income
Last year's taxable income = (x-10,000)
This year's taxable income = (x-40,000)

\(.20(x - 10,000) = .30(x - 40,000)\)
\(.20x - 2,000 = .30x - 12,000\)
\(.10x = 10,000\)
\(x = $100,000\)


Check:
Last year, on $90,000, Jack paid (.20)($90,000) = $18,000

This year, on $100,000, he paid (.30)($60,000) = $18,000. That's a match.

He earned $100,000 this year.

Answer D

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Earlier, the tax laws of a country required one of pay flat 20% of one [#permalink]

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New post 26 Nov 2017, 02:15
[quote="pushpitkc"]Earlier, the tax laws of a country required one of pay flat 20% of one's income. Recently, the concept of progressive tax was implemented and one now needs to pay 30% income tax on the part of one's income above $40000. Jack paid the same amount of tax this year although he earned $10000 more than he did the previous year. What was Jack's income this year?

A. $70000
B. $80000
C. $90000
D. $100000
E. $120000


Lets i be the amount of money Jack earned last year, i + 10,000 earned this year. Progressive tax formula on wealthy looks like this:
0.3( income - 40,000) ; and taxes previous year = taxes this year.

\(0.2i = 0.3(i - 40,000 + 10,000)\)
\(0.2i = 0.3i - 30,000 * 0.3\)
\(-0.1i = - 9,000\)
\(i = 90,000\)

i + 10,000 earned this year => $90,000 + $10,000 = $100,000
The answer is D

Kudos [?]: 2 [0], given: 57

Earlier, the tax laws of a country required one of pay flat 20% of one   [#permalink] 26 Nov 2017, 02:15
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