Income Calculation Breakdown

This problem involves calculating a person's total monthly income based on a series of deductions: a donation and a bank deposit. We are given the final amount remaining and need to work backward to find the initial income.

Understanding the Financial Steps

Let's denote the man's total monthly income as '$M$'.

• Donation: He donates 5% of his monthly income. The amount donated is calculated as:

  Amount donated = $5\%$ of $M = \frac{5}{100} \times M = 0.05M$

• Income Remaining After Donation: After the donation, the income left is:

  Remaining income = $M - 0.05M = (1 - 0.05)M = 0.95M$

• Bank Deposit: He deposits 20% of the *remaining* income. The amount deposited is:

  Amount deposited = $20\%$ of $0.95M = \frac{20}{100} \times (0.95M) = 0.20 \times 0.95M = 0.19M$

• Final Amount Left: The amount he is left with is the income remaining after donation minus the amount deposited.

  Final amount = Remaining income - Amount deposited

  Final amount = $0.95M - 0.19M = (0.95 - 0.19)M = 0.76M$

  Alternatively, if he deposits 20% of the remaining income, he is left with $100\% - 20\% = 80\%$ of the remaining income. So, the final amount is:

  Final amount = $80\%$ of $0.95M = \frac{80}{100} \times 0.95M = 0.80 \times 0.95M = 0.76M$

Solving for Monthly Income

We are given that the final amount left is Rs. 14,250. Using the calculation above, we can set up the equation:

$$0.76M = 14,250$$

To find the monthly income '$M$', we need to divide the final amount by 0.76:

$$M = \frac{14,250}{0.76}$$

To perform the division, we can rewrite 0.76 as a fraction:

$$M = \frac{14,250}{\frac{76}{100}} = 14,250 \times \frac{100}{76}$$

Now, calculate the value:

$$M = \frac{1,425,000}{76}$$

$$M = 18,750$$

Therefore, the man's monthly income is Rs. 18,750.

Verification

Let's check our answer:

• Monthly Income = Rs. 18,750
• Donation (5%) = $0.05 \times 18,750 = 937.50$
• Remaining Income = $18,750 - 937.50 = 17,812.50$
• Deposit (20% of remaining) = $0.20 \times 17,812.50 = 3,562.50$
• Amount Left = $17,812.50 - 3,562.50 = 14,250$

The calculated amount left matches the given amount, confirming our result.