Understanding Rohit's Income Distribution

This problem involves calculating Rohit's total monthly income based on how he distributes it among charity, various expenses, and savings. We are given the percentage of income allocated to each category and the actual amount saved.

The key is to understand that some percentages (food, rent, bills, clothing, savings) are calculated from the remaining income after the charity donation, not from the total monthly income.

Breaking Down the Percentages

Let's list the percentages given:

• Donated to charity: 15% of total income.
• Remaining income: 100% - 15% = 85% of total income.

The remaining 85% is then spent as follows:

• Food: 35% of the remaining income.
• Rent: 20% of the remaining income.
• Bills: 17% of the remaining income.
• Clothing: 8% of the remaining income.
• Savings: The remaining portion of the remaining income.

Calculating the Percentage Saved from Remaining Income

First, let's find the total percentage of the remaining income that is spent on expenses:

Total percentage spent from remaining income = Percentage on Food + Percentage on Rent + Percentage on Bills + Percentage on Clothing

Total percentage spent from remaining income = $35\% + 20\% + 17\% + 8\%$

Total percentage spent from remaining income = $80\%$ of the remaining income.

Now, we can find the percentage of the remaining income that is saved:

Percentage saved from remaining income = 100% (remaining income) - Total percentage spent from remaining income

Percentage saved from remaining income = $100\% - 80\% = 20\%$ of the remaining income.

Relating Savings Amount to Total Income

We know that Rohit saves 20% of his remaining income, and the remaining income is 85% of his total monthly income. So, the amount saved is 20% of 85% of his total monthly income.

Let Rohit's total monthly income be $I$.

• Remaining income = $85\%$ of $I = 0.85 \times I$.
• Amount saved = $20\%$ of (Remaining income) = $20\%$ of ($0.85 \times I$).
• Amount saved = $0.20 \times 0.85 \times I$.

Calculating $0.20 \times 0.85$:

$0.20 \times 0.85 = \frac{20}{100} \times \frac{85}{100} = \frac{1}{5} \times \frac{85}{100} = \frac{85}{500} = \frac{17}{100} = 0.17$.

So, the amount saved is 17% of Rohit's total monthly income ($0.17 \times I$).

Calculating Total Monthly Income

We are given that the amount saved each month is ₹14,620.

Therefore, we can set up the equation:

$0.17 \times I = 14620$

To find $I$, we divide the amount saved by the percentage (as a decimal) it represents of the total income:

$I = \frac{14620}{0.17}$

To make the division easier, we can multiply both the numerator and the denominator by 100:

$I = \frac{14620 \times 100}{0.17 \times 100} = \frac{1462000}{17}$

Now, we perform the division:

$1462000 \div 17$

So, $I = 86000$.

Rohit's total monthly income is ₹86,000.

Verification

Let's quickly check if the numbers add up with a total income of ₹86,000.

• Charity: 15% of 86000 = $0.15 \times 86000 = ₹12,900$.
• Remaining income: $86000 - 12900 = ₹73,100$. (Or $85\%$ of $86000 = 0.85 \times 86000 = ₹73,100$)

Now, let's calculate savings from the remaining income:

• Percentage saved from remaining income is 20%.
• Amount saved = 20% of ₹73,100 = $0.20 \times 73100 = ₹14,620$.

This matches the amount given in the problem. Thus, our calculation is correct.

Conclusion on Rohit's Monthly Income

Based on the detailed breakdown of expenses and savings as percentages of the total and remaining income, and using the given savings amount, we calculated Rohit's total monthly income. The calculation confirms that his monthly income is ₹86,000.

Revision Table: Key Percentages

Additional Information: Understanding Income Distribution Problems

Income distribution problems often test your ability to work with percentages relative to different base amounts (total income vs. remaining income). It's crucial to read carefully and identify which percentage applies to which base.

• Sequential Percentages: When a percentage is taken from the "remaining" amount after a previous deduction, you must calculate the value of the remaining amount first, or multiply the percentages applied sequentially to the original total. For example, 20% of 85% is $(0.20) \times (0.85) = 0.17$, meaning it's 17% of the original amount.
• Sum of Percentages: Percentages that apply to the same base amount can be added together. In this problem, the percentages for food, rent, bills, clothing, and savings all apply to the "remaining income", so their percentages ($35\%+20\%+17\%+8\%+20\%$) should add up to 100% of that remaining income, which they do ($80\%+20\%=100\%$).
• Using Variables: Representing the unknown total income with a variable (like $I$) and setting up an equation based on the given information (like the savings amount) is a standard and reliable way to solve such problems.