An agent gets `5%` commission on all sales up to Rs.10000 and `4%` commission on all sales exceeding this amount. He gives Rs. 31100 from his sales to his company after deducting his commission. Find his total sales.

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Define the total sales
Let the total sales of the agent be \( X \).

### Step 2: Calculate the commission on the first Rs. 10,000
The agent earns a commission of \( 5\% \) on the first Rs. 10,000.
So, the commission on Rs. 10,000 is:
\[ \text{Commission on Rs. 10,000} = 5\% \text{ of } 10,000 = \frac{5}{100} \times 10,000 = 500 \text{ Rs.} \]

### Step 3: Calculate the sales exceeding Rs. 10,000
If the total sales \( X \) exceed Rs. 10,000, the amount exceeding Rs. 10,000 is \( X - 10,000 \).

### Step 4: Calculate the commission on the excess sales
The agent earns a commission of \( 4\% \) on the sales exceeding Rs. 10,000.
So, the commission on the excess sales is:
\[ \text{Commission on excess sales} = 4\% \text{ of } (X - 10,000) = \frac{4}{100} \times (X - 10,000) = 0.04(X - 10,000) \]

### Step 5: Total commission earned by the agent
The total commission earned by the agent is the sum of the commission on the first Rs. 10,000 and the commission on the excess sales:
\[ \text{Total Commission} = 500 + 0.04(X - 10,000) \]

### Step 6: Relate total sales to the amount given to the company
According to the problem, the agent gives Rs. 31,100 to the company after deducting his commission. Therefore, we can set up the equation:
\[ X - \text{Total Commission} = 31,100 \]
Substituting the expression for Total Commission:
\[ X - \left(500 + 0.04(X - 10,000)\right) = 31,100 \]

### Step 7: Simplify the equation
Expanding the equation:
\[ X - 500 - 0.04X + 400 = 31,100 \]
Combine like terms:
\[ X - 0.04X - 100 = 31,100 \]
This simplifies to:
\[ 0.96X - 100 = 31,100 \]

### Step 8: Solve for \( X \)
Add 100 to both sides:
\[ 0.96X = 31,200 \]
Now, divide both sides by 0.96:
\[ X = \frac{31,200}{0.96} \]
Calculating this gives:
\[ X = 32,500 \]

### Conclusion
The total sales of the agent is Rs. 32,500.

---