Certainly! Let's work through the problem step by step.
### (i) One Day Salary Last Year:
Mr. Shivahari's daily household expenses last year were Rs 300, which was given as [tex]\(\frac{3}{10}\)[/tex] (or 30%) of his one day salary.
To find his one day salary, let's denote his one day salary as [tex]\( S \)[/tex].
We have the equation:
[tex]\[ \frac{3}{10} S = 300 \][/tex]
To solve for [tex]\( S \)[/tex], we multiply both sides of the equation by [tex]\( \frac{10}{3} \)[/tex]:
[tex]\[ S = 300 \times \frac{10}{3} \][/tex]
[tex]\[ S = 1000 \][/tex]
Therefore, his one day salary last year was Rs 1000.
### (ii) Daily Expenses This Year:
This year, Mr. Shivahari's daily expenses are [tex]\(\frac{2}{5}\)[/tex] (or 40%) of his one day salary.
Using the one day salary [tex]\( S \)[/tex] found in part (i):
[tex]\[ S = 1000 \][/tex]
His daily expenses this year are:
[tex]\[ \frac{2}{5} \times 1000 \][/tex]
Calculating it:
[tex]\[ \frac{2}{5} \times 1000 = 400 \][/tex]
So, his daily expenses this year amount to Rs 400.
### (iii) Income Saved in One Month:
Mr. Shivahari has to pay Rs 7500 per month as house rent. We need to calculate how much income he saves in one month (30 days).
First, let's find his one month salary. Since there are 30 days in a month:
[tex]\[ \text{Monthly Salary} = 1000 \times 30 = 30000 \][/tex]
Next, calculate his total monthly expenses.
His daily expenses this year are Rs 400, so his total monthly expenses are:
[tex]\[ 400 \times 30 = 12000 \][/tex]
Now, we have to consider house rent. He pays Rs 7500 per month. Therefore, the total expenses, including house rent, are:
[tex]\[ 7500 + 12000 = 19500 \][/tex]
Finally, to find his income saved in one month, we subtract the total expenses from his monthly salary:
[tex]\[ \text{Income Saved per Month} = 30000 - 19500 = 10500 \][/tex]
So, Mr. Shivahari saves Rs 10500 in one month.
