Ketan deposits `10%` of his salary in PF. He saves `40%` of the remaining. The ratio of his expense on entertainment and groceries is 4:5 of the remaining salary after saving. If his expense on the entertainment was ₹2400. Find the monthly salary.

Options

A. ₹10000
B. ₹15000
C. ₹30,000
D. ₹20000

Answer

To solve the problem step-by-step, we will break down Ketan's salary and expenses systematically.

### Step 1: Define Ketan's Monthly Salary
Let Ketan's monthly salary be represented as \( S \).

### Step 2: Calculate the Amount Deposited in PF
Ketan deposits \( 10\% \) of his salary in PF:
\[ \text{Amount deposited in PF} = 0.10S \]

### Step 3: Calculate the Remaining Salary After PF
The remaining salary after the PF deposit is:
\[ \text{Remaining Salary} = S - 0.10S = 0.90S \]

### Step 4: Calculate the Amount Saved
Ketan saves \( 40\% \) of the remaining salary:
\[ \text{Amount saved} = 0.40 \times 0.90S = 0.36S \]

### Step 5: Calculate the Remaining Salary After Saving
The remaining salary after saving is:
\[ \text{Remaining Salary after Saving} = 0.90S - 0.36S = 0.54S \]

### Step 6: Set Up the Ratio of Expenses
The ratio of Ketan's expenses on entertainment and groceries is \( 4:5 \). Let the expenses on entertainment be \( 4x \) and on groceries be \( 5x \).

### Step 7: Calculate Total Expenses
The total expenses on entertainment and groceries can be expressed as:
\[ \text{Total Expenses} = 4x + 5x = 9x \]

### Step 8: Relate Entertainment Expense to Given Value
We know Ketan's expense on entertainment is ₹2400:
\[ 4x = 2400 \]

### Step 9: Solve for \( x \)
To find \( x \):
\[ x = \frac{2400}{4} = 600 \]

### Step 10: Calculate Grocery Expense
Now, calculate the grocery expense:
\[ 5x = 5 \times 600 = 3000 \]

### Step 11: Calculate Total Expenses
Now, calculate the total expenses:
\[ \text{Total Expenses} = 2400 + 3000 = 5400 \]

### Step 12: Set Up the Equation
Since the total expenses equal the remaining salary after saving:
\[ 5400 = 0.54S \]

### Step 13: Solve for \( S \)
Now, solve for \( S \):
\[ S = \frac{5400}{0.54} = 10000 \]

### Conclusion
Ketan's monthly salary is ₹10,000.

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