Shweta spends 21% of her monthly salary on house rent, 14% on education, and 13% on entertainment, and still saves ₹5,408. What is her monthly salary (in)?
Understanding Shweta's Monthly Salary Calculation
This problem requires us to calculate Shweta's total monthly salary. We are given information about the percentages of her salary she spends on various items like house rent, education, and entertainment. We are also given the exact amount she saves after these expenses.
Calculating Total Expenses Percentage
First, let's sum up the percentages of the salary Shweta spends:
- House Rent: 21%
- Education: 14%
- Entertainment: 13%
The total percentage of salary spent is the sum of these amounts:
Total Expenses Percentage = $21\% + 14\% + 13\% = 48\%$
Determining the Savings Percentage
A person's total monthly salary represents 100%. To find the percentage of salary saved, we subtract the total expense percentage from 100%:
Savings Percentage = $100\% - \text{Total Expenses Percentage}$
Savings Percentage = $100\% - 48\% = 52\%$
This means Shweta saves 52% of her monthly salary.
Calculating the Actual Monthly Salary
We are told that Shweta saves ₹5,408. We've calculated that this amount represents 52% of her total monthly salary.
Let 'S' denote Shweta's total monthly salary.
We can express the relationship as an equation:
$52\%$ of $S = ₹5,408$
To solve for S, we convert the percentage to a decimal:
$0.52 \times S = 5408$
Now, we isolate S by dividing the savings amount by the decimal value of the savings percentage:
$S = \frac{5408}{0.52}$
To simplify the division, we can multiply the numerator and denominator by 100:
$S = \frac{5408 \times 100}{0.52 \times 100} = \frac{540800}{52}$
Performing the division:
$S = 10400$
Final Answer for Monthly Salary
Therefore, Shweta's monthly salary is ₹10,400.
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