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 answer is 48000 (Option 48000).

Step-by-Step Explanation:

Step 1: Assume the Total Monthly Income

Let the man's total monthly income be $X$ rupees.

Step 2: Calculate Expenditure on Rent

The man spends 20% of his total monthly income on rent.

$\text{Rent}=20\%\text{ of }X=\frac{20}{100}\times X=0.20X$

Step 3: Calculate the Remaining Income

After paying the rent, the remaining income is:

$\text{Remaining Income}=X-0.20X=0.80X$

Step 4: Calculate Expenditure on Food

He spends 10% of the remaining income on food.

$\text{Food}=10\%\text{ of }0.80X=\frac{10}{100}\times 0.80X=0.08X$

Step 5: Calculate Total Savings

The total savings after paying for rent and food will be:

$\text{Savings}=\text{Remaining Income}-\text{Food}$

$\text{Savings}=0.80X-0.08X=0.72X$

Step 6: Equate Savings to the Given Amount and Find Monthly Income

We are given that he saves Rs. 34,560.

$0.72X=34560$

$X=\frac{34560}{0.72}$

$X=\frac{3456000}{72}=48000$

Thus, his total monthly income is Rs. 48,000.