Question

A peerson spends 75% of his income. If his income increases by 20% and expenses increase by 15%then find the percent increase in savings

Answer 1

Answer:

35%

Step-by-step explanation:

Let the income be x.

Therefore, expenditure = 75% of x = 75x/100

So, savings = income - expenditure = x - 75x/100 = 25x/100

After increasing income by 20%, new income = x + 20% of x = x + 20x/100

                                                                                                     = 120x/100 = 6x/5

If expenditure increase by 15%, then new expenditure

= 75x/100 + 15% of 75x/100 = 75x/100 + 15*75*x/100*100

                                             = 75x/100*(1 + 15/100) = 75x/100*115/100 = 69x/80

Therefore, new savings = new income - new expenditure

                                        = 6x/5 - 69x/80 = 27x/80

So, percentage increase in savings = (27x/80 - 25x/100)/(25x/100) * 100

                                                           = (35x/400)/(25x/100) * 100

                                                           = 35/100 * 100 = 35%

Answer 2

AnsWer:

$:\implies\sf 35\;\%$

$\rule{150}{2}$

Now,

$\;\;\bullet$ Let income of the person be Rs. 100

$\star\;{\underline{\sf{\pink{As\;per\;given\;question\;:}}}}$

$\;\;\bullet$ Expenditure of the person = 75% = $\bf{75\;\%}$

Therefore,

☯ Saving of the person -

$\maltese\;{\boxed{\sf{ s_1 = 100 - 75}}}\\\\:\implies{\boxed{\sf{\purple{Rs.\;25}}}}\;\bigstar$

$\rule{150}{2}$

☯ When, his income increased by 20%

$:\implies\sf 100 + \frac{100 \times 20}{100}\\\\:\implies\sf 100 + \frac{20 \cancel{00}}{ \cancel{100}}\\\\:\implies\sf 100 + 20\\\\:\implies{\boxed{\sf{\purple{Rs.\;120}}}}\;\bigstar$

☯If his expenditure increased by 15%

$:\implies\sf 75 + \frac{75 \times 15}{100}\\\\:\implies\sf 75 + \frac{1125}{100}\\\\:\implies\sf 100 + 11.25\\\\:\implies{\boxed{\sf{\purple{Rs.\;86.25}}}}\;\bigstar$

Therefore,

☯ Saving of the person -

$\maltese\;{\boxed{\sf{ s_2 = 120 - 86.25}}}\\\\:\implies{\boxed{\sf{\red{Rs.\;33.75}}}}\;\bigstar$

$\rule{150}{2}$

☯ Here, we get -

$\;\;\bullet\;\sf s_1 = Rs. \;25$

$\;\;\bullet\;\sf s_2 = Rs. \;33.75$

$\normalsize\therefore\sf \underline{Increasement\;in\;saving\;:}$

$:\implies\sf s_2 - s_1 \\\\:\implies\sf 33.75 - 25\\\\:\implies{\boxed{\sf{\blue{Rs.\;8.75}}}}\;\bigstar$

$\normalsize\therefore\sf \underline{Percentage\;Increase\;:}$

$:\implies\sf \frac{8.75}{25} \times 100\\\\:\implies\sf 0.35 \times 100\\\\:\implies{\boxed{\bf{\blue{35\;\%}}}}\;\bigstar$

$\sf\dag\; \underline{Hence,\; Percentage\;increase\;in\;savings\;is\; \bf{35\;\%}}$