A man spends 15% of his monthly income on rent and 40% of the remainde

1.	A man spends 15% of his monthly income on rent and 40% of the remainder on clothes. If the monthly savings are Rs.306, find his aanual income
Answer» A man SPENDS 15% of his monthly income on rent. The annual income is RS 7200 Solution: GIVEN, a man spends 15% of his monthly income on rent and 40% of the REMAINDER on clothes. The monthly savings are Rs.306. We have to find his annual income. Now, his monthly income = rent payment + clothes payment + monthly savings Monthly income = 15% of Monthly income + 40% of (monthly income – rent payment) + 306 rupees Let monthly income = "m" m = 15% of m +40% of m – 40% of 15% of m + 306 $\mathrm{m}=\frac{15}{100} \times \mathrm{m}+\frac{40}{100} \times \mathrm{m}-\frac{40}{100} \times \frac{15}{100} \times \mathrm{m}+306$ $\mathrm{m}=\mathrm{m}\left(\frac{15}{100}+\frac{40}{100}-\frac{40}{100} \times \frac{15}{100}\right)+306$ $m-m\left(\frac{55}{100}-\frac{2}{5} \times \frac{15}{100}\right)=306$ $m\left(1-\frac{55}{100}+2 \times \frac{3}{100}\right)=306$ On simplification we GET, $m\left(1-\frac{55}{100}+\frac{6}{100}\right)=306$ $\mathrm{m}\left(1-\frac{49}{100}\right)=306$ $\begin{array}{l}{\mathrm{m} \times \frac{51}{100}=306} \\\\ {\mathrm{m}=306 \times \frac{100}{51}=600}\end{array}$ Hence monthly income = 600 So, annual income = 12 x 600 = 7200 Hence, annual income of the person is RS 7200

A man spends 15% of his monthly income on rent and 40% of the remainder on clothes. If the monthly savings are Rs.306, find his aanual income

Answer»

Solution:

GIVEN, a man spends 15% of his monthly income on rent and 40% of the REMAINDER on clothes.

The monthly savings are Rs.306. We have to find his annual income.

Now, his monthly income = rent payment + clothes payment + monthly savings

Monthly income = 15% of Monthly income + 40% of (monthly income – rent payment) + 306 rupees

Let monthly income = "m"

m = 15% of m +40% of m – 40% of 15% of m + 306

$\mathrm{m}=\frac{15}{100} \times \mathrm{m}+\frac{40}{100} \times \mathrm{m}-\frac{40}{100} \times \frac{15}{100} \times \mathrm{m}+306$

$\mathrm{m}=\mathrm{m}\left(\frac{15}{100}+\frac{40}{100}-\frac{40}{100} \times \frac{15}{100}\right)+306$

$m-m\left(\frac{55}{100}-\frac{2}{5} \times \frac{15}{100}\right)=306$

$m\left(1-\frac{55}{100}+2 \times \frac{3}{100}\right)=306$

On simplification we GET,

$m\left(1-\frac{55}{100}+\frac{6}{100}\right)=306$

$\mathrm{m}\left(1-\frac{49}{100}\right)=306$

$\begin{array}{l}{\mathrm{m} \times \frac{51}{100}=306} \\\\ {\mathrm{m}=306 \times \frac{100}{51}=600}\end{array}$

Hence monthly income = 600

So, annual income = 12 x 600 = 7200

Hence, annual income of the person is RS 7200