Pradeep spends 40 percent of his monthly income on food items and 50 percent of the remaining on cloths and conveyance. He saves one-third of the remaining amount after spending on food. Clothes and conveyance. If he saves Rs. 19,200 every year. What is his monthly income?

Options

A. Rs.24000
B. Rs.12000
C. Rs.16000
D. Rs.20000

Answer

To find Pradeep's monthly income, we will break down the problem step by step.

### Step 1: Determine the amount spent on food
Pradeep spends 40% of his monthly income on food items. Let's denote his monthly income as \( I \).

Amount spent on food = \( 0.40 \times I \)

### Step 2: Calculate the remaining income after food expenses
After spending on food, the remaining income is:

Remaining income = \( I - 0.40I = 0.60I \)

### Step 3: Calculate the amount spent on clothes and conveyance
Pradeep spends 50% of the remaining income on clothes and conveyance.

Amount spent on clothes and conveyance = \( 0.50 \times 0.60I = 0.30I \)

### Step 4: Calculate the remaining income after clothes and conveyance expenses
Now, we calculate the remaining income after spending on clothes and conveyance:

Remaining income = \( 0.60I - 0.30I = 0.30I \)

### Step 5: Determine the amount saved
Pradeep saves one-third of the remaining amount after spending on food, clothes, and conveyance.

Amount saved = \( \frac{1}{3} \times 0.30I = 0.10I \)

### Step 6: Set up the equation based on the annual savings
We know that Pradeep saves Rs. 19,200 every year. Therefore, his monthly savings is:

Monthly savings = \( \frac{19200}{12} = 1600 \)

Now we can set up the equation:

\( 0.10I = 1600 \)

### Step 7: Solve for monthly income
To find \( I \), we can rearrange the equation:

\( I = \frac{1600}{0.10} = 16000 \)

### Conclusion
Pradeep's monthly income is Rs. 16,000.

---