A person saves 6% of his income. Two years later, his income shoots up by 22% but his savings remain the same. Find the hike in his expendit

Question

A person saves 6% of his income. Two years later, his income shoots up by 22% but his savings remain the same. Find the hike in his expenditure.

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Mary 1 week 2021-09-14T06:27:09+00:00 1 Answer 0 views 0

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    2021-09-14T06:28:10+00:00

    Answer:

    let the income be x

    savings = 6%

    expenditure =(\frac{6}{100} \times x)+x\\\\=\frac{6x}{100} +\frac{x(100)}{1(100)} \\\\=\frac{6x}{100}+\frac{100x}{100}\\\\=\frac{106x}{100}

    after two years,

    income increase = 22%

    ∴ income increase =\frac{22x}{100\\}

         

    total \: income = x+\frac{22x}{100}\\\\ =\frac{100x+22x}{100} \\\\=\frac{122x}{100}

    income saved = 6%

    expenditure =(\frac{122x}{100} \times \frac{6}{100})  + \frac{122x}{100}  \\\\      =\frac{732x}{10000}+ \frac{122x}{100}\\\\=\frac{732x}{10000}+ \frac{122x(100)}{100(100)}\\\\=\frac{732x}{10000}+\frac{12200x}{10000}\\\\=\frac{732x+12200x}{10000}\\\\=\frac{12932x}{10000}\\[tex]expenditure\ hike = expenditure\ of\ present\ year – expenditure\ two\\ years \ later\\ = \frac{12932x}{10000}-\frac{106x}{100} \\\\= \frac{12932x}{10000}-\frac{106x(100)}{100(100)} \\\\= \frac{12932x}{10000}-\frac{10600x}{10000} \\\\=\frac{12932x-10600x}{10000}\\\\=\frac{2332x}{10000}\\\\=\frac{583x(4)}{2500(4)}\\\\=\frac{583x}{2500}\\\\[/tex]

    Step-by-step explanation:

    Thus expenditure hike is \frac{583}{25}%\\%

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