Nikhil gets a commission of `5%` upto the sell of `Rs.10000` and above this he gets `4%` commisssion on the sale. If after deducting his commisssion he deposits `Rs.31100` to company . Find his total sale.

Options

A. `32500`
B. `35500`
C. `45500`
D. `32500`

Answer

To find Nikhil's total sale, we can break down the problem step by step.

### Step 1: Define the total sale
Let the total sale be Rs. \( x \).

### Step 2: Calculate the commission for the first Rs. 10,000
Nikhil earns a commission of 5% on the first Rs. 10,000.
\[ \text{Commission on Rs. 10,000} = \frac{5}{100} \times 10,000 = 500 \text{ Rs.} \]

### Step 3: Calculate the commission for sales above Rs. 10,000
For sales above Rs. 10,000, Nikhil earns a commission of 4%. The amount above Rs. 10,000 is \( x - 10,000 \).
\[ \text{Commission on sales above Rs. 10,000} = \frac{4}{100} \times (x - 10,000) = 0.04(x - 10,000) \]

### Step 4: Calculate the total commission
Now, we can find the total commission by adding the commission from the first Rs. 10,000 and the commission from the sales above Rs. 10,000.
\[ \text{Total Commission} = 500 + 0.04(x - 10,000) \]

### Step 5: Set up the equation for the amount deposited
After deducting his commission, Nikhil deposits Rs. 31,100 to the company. Therefore, we can set up the equation:
\[ x - \left(500 + 0.04(x - 10,000)\right) = 31,100 \]

### Step 6: Simplify the equation
Expanding the equation:
\[ x - 500 - 0.04x + 400 = 31,100 \]
Combine like terms:
\[ x - 0.04x - 500 + 400 = 31,100 \]
This simplifies to:
\[ 0.96x - 100 = 31,100 \]

### Step 7: Solve for \( x \)
Now, add 100 to both sides:
\[ 0.96x = 31,200 \]
Now, divide by 0.96:
\[ x = \frac{31,200}{0.96} = 32,500 \]

### Final Answer
Thus, Nikhil's total sale is Rs. 32,500.

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