A man spends 20% of his monthly income on rent and 10% of the remaining income on food. If he saves Rs. 34,560, then find his monthly income (in Rs).

The correct option is 48000.

Let's break down the problem step-by-step to find the man's total monthly income.

Step 1: Define the total income
Let the man's total monthly income be represented as $x$ rupees.

Step 2: Calculate expenditure on rent
The man spends 20% of his monthly income on rent.
$\text{Rent expense}=20\%\text{of}x=\frac{20}{100}\times x=0.2x$

Step 3: Find the remaining income
After paying the rent, the remaining income is:
$\text{Remaining income}=x-0.2x=0.8x$

Step 4: Calculate expenditure on food
He spends 10% of the remaining income on food.
$\text{Food expense}=10\%\text{of}0.8x=\frac{10}{100}\times 0.8x=0.08x$

Step 5: Calculate the remaining total savings
The savings after spending on rent and food will be:
$\text{Savings}=\text{Remaining income}-\text{Food expense}$
$\text{Savings}=0.8x-0.08x=0.72x$

Step 6: Equate savings to the given value and solve for $x$
We are given that the total savings equal Rs. 34,560.
$0.72x=34560$

Solving for $x$:
$x=\frac{34560}{0.72}$
$x=\frac{3456000}{72}=48000$

Therefore, the man's total monthly income is Rs. 48,000.