Calculating Monthly Salary Based on Expenses

Let's break down how to find Vignesh's monthly salary based on his spending habits and the additional expense he incurred.

First, we need to understand the different categories of expenses Vignesh has from his regular monthly salary:

• Food: 42%
• House Rent: 16%
• Entertainment: 11%
• Conveyance: 7%

We can calculate the total percentage of his salary that Vignesh spends regularly on these items.

Total regular spending percentage $ = \text{Percentage on Food} + \text{Percentage on House Rent} + \text{Percentage on Entertainment} + \text{Percentage on Conveyance} $

Total regular spending percentage $ = 42\% + 16\% + 11\% + 7\% $

Total regular spending percentage $ = 76\% $

This means 76% of his monthly salary is spent on these fixed categories.

Now, let's consider the family function expense. The total expense for the function was Rs. 18,000. Vignesh borrowed Rs. 12,000 from a money lender. This implies that the remaining amount for the family function came from his monthly salary.

Amount used from salary for family function $ = \text{Total Function Expense} - \text{Amount Borrowed} $

Amount used from salary for family function $ = \text{Rs. } 18,000 - \text{Rs. } 12,000 $

Amount used from salary for family function $ = \text{Rs. } 6,000 $

This amount of Rs. 6,000 must represent the portion of his salary that was not spent on the regular categories (food, rent, entertainment, conveyance).

The percentage of salary remaining after regular spending is calculated as:

Percentage of salary remaining $ = 100\% - \text{Total regular spending percentage} $

Percentage of salary remaining $ = 100\% - 76\% $

Percentage of salary remaining $ = 24\% $

So, 24% of Vignesh's monthly salary is equal to the Rs. 6,000 he used for the family function from his salary.

Let 'S' represent Vignesh's monthly salary.

We can set up the equation:

$ 24\% \text{ of } S = \text{Rs. } 6,000 $

To solve for S, we convert the percentage to a decimal or fraction:

$ \frac{24}{100} \times S = 6000 $

Now, we isolate S by multiplying both sides by $\frac{100}{24}$:

$ S = \frac{6000 \times 100}{24} $

$ S = \frac{600000}{24} $

Let's perform the division:

$ S = 25000 $

Therefore, Vignesh's monthly salary is Rs. 25,000.

We can verify this:

• Regular spending (76% of Rs. 25,000) $ = 0.76 \times 25000 = 19000 $
• Amount remaining (24% of Rs. 25,000) $ = 0.24 \times 25000 = 6000 $
• Total salary $ = 19000 + 6000 = 25000 $

The remaining amount of Rs. 6,000 is exactly what he used from his salary for the family function, along with the Rs. 12,000 borrowed to cover the Rs. 18,000 expense.

Revision Table: Key Calculations

Additional Information: Understanding Percentage Problems

Percentage problems often involve finding a part of a whole or finding the whole when a part and its percentage are known. In this case, we knew a part (Rs. 6,000) and the percentage it represents (24%), and we needed to find the whole (the monthly salary).

The key is to correctly identify what percentage corresponds to what amount. Here, the amount used from savings for the unexpected expense corresponds to the percentage of salary left after regular expenses.

Formula used: If P% of a quantity Q is A, then $ \frac{P}{100} \times Q = A $. We can rearrange this to find Q if P and A are known: $ Q = \frac{A \times 100}{P} $.

In this problem, A = Rs. 6,000 and P = 24%, so $ Q = \frac{6000 \times 100}{24} $, which gave us the monthly salary.