a man spends 15% of his monthly income on clothes and 40% of the rest on food he device saves 153 rupees find his monthly income
Answers
Step-by-step explanation:
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}+306m=
100
15
×m+
100
40
×m−
100
40
×
100
15
×m+306
\mathrm{m}=\mathrm{m}\left(\frac{15}{100}+\frac{40}{100}-\frac{40}{100} \times \frac{15}{100}\right)+306m=m(
100
15
+
100
40
−
100
40
×
100
15
)+306
m-m\left(\frac{55}{100}-\frac{2}{5} \times \frac{15}{100}\right)=306m−m(
100
55
−
5
2
×
100
15
)=306
m\left(1-\frac{55}{100}+2 \times \frac{3}{100}\right)=306m(1−
100
55
+2×
100
3
)=306
On simplification we get,
m\left(1-\frac{55}{100}+\frac{6}{100}\right)=306m(1−
100
55
+
100
6
)=306
\mathrm{m}\left(1-\frac{49}{100}\right)=306m(1−
100
49
)=306
\begin{gathered}\begin{array}{l}{\mathrm{m} \times \frac{51}{100}=306} \\\\ {\mathrm{m}=306 \times \frac{100}{51}=600}\end{array}\end{gathered}
m×
100
51
=306
m=306×
51
100
=600
Hence monthly income = 600
So, annual income = 12 x 600 = 7200
Hence, annual income of the person is RS 7200