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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

Updated On: Jan 15, 2026
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Solution and Explanation

To establish the problem, we proceed step by step:

Assume Amal procures \(x\) pens at 8 rupees per pen.

The aggregate cost for the pens is \(8x\) rupees. Additionally, an employee is engaged at a fixed wage \(W\).

100 pens are subsequently sold at 12 rupees each, yielding revenue of \(1200\) rupees.

This leaves \(x - 100\) pens remaining.

Scenario 1:

If the remaining pens are sold at 11 rupees each:

Revenue generated is \(11(x - 100)\) rupees.

The total revenue accumulates to \(1200 + 11(x - 100)\).

The net profit, calculated as Revenue minus Total Cost minus Wage, is \(300\) rupees.

\(1200 + 11x - 1100 - 8x - W = 300\)

This simplifies to \(3x - W = 200\)...(i)

Scenario 2:

If the remaining pens are sold at 9 rupees each:

Revenue generated is \(9(x - 100)\) rupees.

The total revenue accumulates to \(1200 + 9(x - 100)\).

A net loss of \(300\) rupees is incurred, defined as Total Cost plus Wage minus Revenue.

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

This simplifies to \(( -x + W = 400 )\) ...(ii)

Simultaneous resolution of equations (i) and (ii) is performed:

Adding both equations yields:

\(2x = 600\)

Therefore, \(x = 300\).

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

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

\(900 - W = 200\)

Consequently, \(W = 700\).

The employee's wage is thus determined to be 700 INR.

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