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 \(= 8n+W\)
Where, \(W\)= wage. 

First case:
SP \(= 12 \times 100 + 11 \times  (n - 100)\)
Given that, the profit is 300, then
\(1200+11n-1100-8n-W=300\)
\(3n-W = 200\)      ……. (1)

In second case:
\(1200+9n-900-8n-W=-300\)    (Loss)
\(W-n = 600\)      …….. (2)
On adding eq (1) & eq (2)
\(2n = 800\)
\(n = \frac {800}{2}\)
\(n = 400\)
Thus, the wage of the employee,
\(W = 600 + 400\)
\(W=1000 \)

So, the answer is Rs. \(1000\)