Income Calculation Using Percentages

This problem involves calculating Ramagya's total income based on his spending on house rent and household expenses, and the amount he saves. We need to work backward from the savings to find the initial income.

Understanding the Spending

Let's break down Ramagya's expenses:

• He spends 22% of his salary on house rent.
• He spends 75% of the *remaining* salary on household expenses.
• The final amount left is his savings, which is ₹3,705.

Step-by-Step Calculation

We can represent Ramagya's total income as '$I$'.

1. Calculate remaining salary after house rent:

   If 22% is spent on rent, the remaining percentage is $100\% - 22\% = 78\%$.

   Remaining salary = $78\%$ of Total Income = $0.78 \times I$.

2. Calculate household expenses:

   He spends 75% of the *remaining* salary ($0.78 \times I$) on household expenses.

   Household Expenses = $75\%$ of $(0.78 \times I) = 0.75 \times (0.78 \times I)$.

3. Calculate the percentage saved:

   The amount saved is the remaining salary after rent, minus the household expenses.

   Amount Saved = (Remaining Salary after Rent) - (Household Expenses)

   Amount Saved = $(0.78 \times I) - (0.75 \times 0.78 \times I)$

   We can factor out $(0.78 \times I)$:

   Amount Saved = $(0.78 \times I) \times (1 - 0.75)$

   Amount Saved = $(0.78 \times I) \times 0.25$

   Amount Saved = $0.195 \times I$.

   So, the savings represent 19.5% of the total income.

4. Find the total income:

   We know that the Amount Saved is ₹3,705, and this equals $0.195 \times I$.

   $$ 3,705 = 0.195 \times I $$

   To find the total income ($I$), we rearrange the equation:

   $$ I = \frac{3,705}{0.195} $$

   $$ I = \frac{3,705,000}{195} $$

   $$ I = 19,000 $$

Summary Table

Conclusion

Ramagya's total income is ₹19,000.