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

Let's set this problem up step by step: 

Let's 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. Revenue from this sale = \(1200\) rupees. 

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

Scenario 1: 

If the remaining pens are sold at 11 rupees each: 

Revenue =\(11(x - 100)\) rupees. 

Total Revenue = \(1200 + 11(x - 100)\). 

Net Profit = Revenue - Total Cost - Wage = \(300\). 

\(1200 + 11x - 1100 - 8x - W = 300\) 

\(3x - W = 200\)..\(.(i) \)

Scenario 2: 

If the remaining pens are sold at 9 rupees each: 

Revenue = \(9(x - 100)\) rupees. 

Total Revenue = \(1200 + 9(x - 100)\). 

Net Loss = Total Cost + Wage - Revenue = \(300\). 

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

\(( -x + W = 400 )\) ...(ii)

Solving equations (i) and (ii) simultaneously, we get: 

Adding both equations: 

\(2x = 600\)

\(x = 300\)

Substituting \(x = 300\) in equation (i): 

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

\(900 - W = 200\)

\(W = 700\)

So, the wage of the employee is 700 INR.

Answer 2

Let the number of pens purchased be \( n \). The total expenses are given by \( 8n + W \), where \( W \) is the wage of the employee.

Step 1: First Case (Profit of 300)

The selling price (SP) in the first case is: \[ SP = 12 \times 100 + 11 \times (n - 100) \] The total profit is given as 300, so we have the equation: \[ 1200 + 11n - 1100 - 8n - W = 300 \] Simplifying: \[ 3n - W = 200 \quad \text{(Equation 1)} \]

Step 2: Second Case (Loss of 300)

In the second case, the selling price is: \[ SP = 1200 + 9n - 900 - 8n - W \] The loss is 300, so we get: \[ W - n = 600 \quad \text{(Equation 2)} \]

Step 3: Solve the system of equations

Adding equation (1) and equation (2): \[ (3n - W) + (W - n) = 200 + 600 \] Simplifying: \[ 2n = 800 \] \[ n = \frac{800}{2} = 400 \]

Step 4: Calculate the wage of the employee

Substituting \( n = 400 \) into equation (2): \[ W - 400 = 600 \] \[ W = 600 + 400 = 1000 \]

Final Answer:

The wage of the employee is \( \boxed{1000} \) rupees.