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:

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.