A man spends 10% of his monthly income on shopping. From the remaining income, he spends 20% on food. After making these expenditures, he saves Rs 7200. Find his total monthly income (in Rs).

The correct answer is 10000.

Step-by-Step Explanation:

Step 1: Define the total monthly income
Let the total monthly income of the man be $x$ Rs.

Step 2: Calculate the remaining income after shopping
The man spends 10% of his monthly income on shopping.
Remaining income after shopping = 100% - 10% = 90% of total income.

$\text{Remaining income after shopping}=\frac{90}{100}\times x=0.9x$

Step 3: Calculate the remaining income (savings) after spending on food
From the remaining income, he spends 20% on food.
Therefore, the remaining percentage of income saved is 100% - 20% = 80% of the income remaining after shopping.

$\text{Savings}=\frac{80}{100}\times 0.9x$

$\text{Savings}=0.8\times 0.9x=0.72x$

Step 4: Find the total monthly income
We are given that his total savings after these expenditures is Rs 7200.

$0.72x=7200$

$x=\frac{7200}{0.72}$

$x=10000$

Thus, the total monthly income of the man is Rs 10000.