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).

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The correct answer is 10000.

Step-by-step explanation:

Let the total monthly income of the man be Rs $x$.

Step 1: Calculate expenditure on shopping.
The man spends 10% of his monthly income on shopping.

$\text{Shopping Expenditure}=10\%\text{of}x=\frac{10}{100}\times x=0.10x$

Step 2: Find the remaining income after shopping.

$\text{Remaining Income}=x-0.10x=0.90x$

Step 3: Calculate expenditure on food.
He spends 20% of the remaining income on food.

$\text{Food Expenditure}=20\%\text{of}0.90x=\frac{20}{100}\times 0.90x=0.18x$

Step 4: Find the final savings fraction.
The amount saved after spending on food is the remaining 80% of the leftover income, or total remaining income minus food expenditure.

$\text{Savings}=0.90x-0.18x=0.72x$

Step 5: Equate savings to the given value and solve for $x$.
According to the problem, the savings equal Rs 7200.

$0.72x=7200$

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

$x=10000$

Thus, his total monthly income is Rs 10,000.