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.

Answer 1

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}$$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}$

Step-by-step explanation:

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