Mr. Hari spends 36% of his income on food items and 25% of the remaining amount on clothes, medical, and conveyance. He saves half of the remaining amount every month. If he saves ₹1,80,000 every year, then find his monthly income.
₹62,500
Detailed Solution: Mr. Hari's Monthly Income Calculation
This solution explains how to determine Mr. Hari's monthly income based on his spending habits and annual savings. We will break down the problem step-by-step using percentages and calculations.
Understanding Mr. Hari's Financial Flow
The question provides information about Mr. Hari's expenses as percentages of his income and the remaining amount after certain expenditures. We are also given his total annual savings and asked to find his monthly income.
Step-by-Step Calculation of Monthly Income
Let's denote Mr. Hari's monthly income as \(I\). We will track the flow of his income:
- Expenditure on Food Items: Mr. Hari spends 36% of his income on food items. Expenditure on food = \(36\%\) of \(I = 0.36 \times I\).
- Income Remaining After Food Expenses: The amount left after spending on food is: Remaining Income = \(I - 0.36I = (1 - 0.36)I = 0.64I\).
- Expenditure on Clothes, Medical, and Conveyance: He spends 25% of the *remaining amount* on these items. Expenditure on these items = \(25\%\) of \((0.64I) = 0.25 \times 0.64I = 0.16I\).
- Income Remaining After All Stated Expenses: The income left after the food and the other specified expenses is: Remaining Income = \((0.64I) - (0.16I) = (0.64 - 0.16)I = 0.48I\).
- Monthly Savings: He saves half of this remaining amount. Monthly Savings = \(0.5 \times (0.48I) = 0.24I\).
Relating Savings to Annual Income
We know that the monthly savings are \(0.24I\). The problem states that he saves ₹1,80,000 every year.
Therefore, the annual savings can be calculated as 12 times his monthly savings:
Annual Savings = \(12 \times (\text{Monthly Savings})\) Annual Savings = \(12 \times (0.24I)\) Annual Savings = \(2.88I\).Finding the Monthly Income (I)
We are given that the Annual Savings = ₹1,80,000.
Equating the two expressions for annual savings:
\(2.88I = 1,80,000\)To find the monthly income \(I\), we rearrange the equation:
\(I = \frac{1,80,000}{2.88}\)To simplify the division, we can write 2.88 as a fraction:
\(2.88 = \frac{288}{100}\)Substituting this back into the equation for \(I\):
\(I = \frac{1,80,000}{\frac{288}{100}}\) \(I = \frac{1,80,000 \times 100}{288}\) \(I = \frac{18,000,000}{288}\)Now, we perform the division:
\(I = 62,500\)So, Mr. Hari's monthly income is ₹62,500.
Summary of Income Distribution (Monthly)
| Category | Percentage of Income | Amount (₹) |
|---|---|---|
| Monthly Income | \(100\%\) | \(62,500\) |
| Food Expenditure | \(36\%\) | \(0.36 \times 62,500 = 22,500\) |
| Remaining After Food | \(64\%\) | \(62,500 - 22,500 = 40,000\) |
| Clothes, Medical, Conveyance | \(25\%\) of \(64\% = 16\%\) | \(0.16 \times 62,500 = 10,000\) |
| Remaining After All Expenses | \(48\%\) | \(40,000 - 10,000 = 30,000\) |
| Monthly Savings | \(50\%\) of \(48\% = 24\%\) | \(0.24 \times 62,500 = 15,000\) |
Let's verify the annual savings:
Monthly Savings = ₹15,000 Annual Savings = \(15,000 \times 12 = 1,80,000\).This matches the given information in the question.
Final Answer
Mr. Hari's monthly income is ₹62,500.
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