Question

Amal purchases some pens at ₹ 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ₹ 12 each. If the remaining pens are sold at ₹ 11each, then he makes a net profit of ₹ 300, while he makes a net loss of ₹ 300 if the remaining pens are sold at ₹ 9 each. The wage of the employee, in INR, is

Answer 1

Correct Answer: 700

Let's set this problem up step by step:

Assume Amal purchases \( x \) pens at 8 rupees each.

Total cost of the pens = \( 8x \) rupees. He hires an employee at a fixed wage \( W \).

He sells 100 pens at 12 rupees each. The revenue from this sale is:

\[ \text{Revenue} = 100 \times 12 = 1200 \, \text{rupees}. \]

Now, there are \( x - 100 \) pens left.

Scenario 1: Selling Remaining Pens at 11 Rupees Each

If the remaining pens are sold at 11 rupees each, the revenue from this sale is:

\[ \text{Revenue} = 11(x - 100) \, \text{rupees}. \]

Total revenue from both sales is:

\[ \text{Total Revenue} = 1200 + 11(x - 100). \]

The net profit is the total revenue minus the total cost and wage, which is given as 300 rupees. Hence, the equation becomes:

\[ 1200 + 11x - 1100 - 8x - W = 300 \]

Simplifying the equation:

\[ 3x - W = 200 \quad \text{...(i)} \]

Scenario 2: Selling Remaining Pens at 9 Rupees Each

If the remaining pens are sold at 9 rupees each, the revenue from this sale is:

\[ \text{Revenue} = 9(x - 100) \, \text{rupees}. \]

Total revenue from both sales is:

\[ \text{Total Revenue} = 1200 + 9(x - 100). \]

The net loss is the total cost and wage minus the total revenue, which is given as 300 rupees. Hence, the equation becomes:

\[ 8x + W - (1200 + 9x - 900) = 300 \]

Simplifying the equation:

\[ -x + W = 400 \quad \text{...(ii)} \]

Step 3: Solving the System of Equations

We now solve equations (i) and (ii) simultaneously:

Adding both equations (i) and (ii):

\[ (3x - W) + (-x + W) = 200 + 400 \]

Simplifying:

\[ 2x = 600 \]

Solving for \( x \):

\[ x = \frac{600}{2} = 300 \]

Step 4: Finding the Wage \(W\)

Substitute \( x = 300 \) into equation (i):

\[ 3(300) - W = 200 \]

Simplifying:

\[ 900 - W = 200 \]

Solving for \( W \):

\[ W = 900 - 200 = 700 \]

Conclusion

The wage of the employee is 700 rupees.