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.