Question:medium

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
Show Solution

Correct Answer: 700

Solution and Explanation

Problem breakdown:

Amal buys \( x \) pens at 8 rupees each, for a total cost of \( 8x \) rupees. He also pays an employee a fixed wage \( W \).

He sells 100 pens at 12 rupees each, generating a revenue of \( 100 \times 12 = 1200 \) rupees.

Remaining pens: \( x - 100 \).

Scenario 1: Remaining Pens Sold at 11 Rupees Each

Revenue from remaining pens: \( 11(x - 100) \) rupees.

Total revenue: \( 1200 + 11(x - 100) \) rupees.

Net profit: Total revenue - Total cost - Wage = 300 rupees.

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

Simplified equation: \( 3x - W = 200 \quad \text{...(i)} \)

Scenario 2: Remaining Pens Sold at 9 Rupees Each

Revenue from remaining pens: \( 9(x - 100) \) rupees.

Total revenue: \( 1200 + 9(x - 100) \) rupees.

Net loss: Total cost + Wage - Total revenue = 300 rupees.

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

Simplified equation: \( -x + W = 400 \quad \text{...(ii)} \)

Step 3: Solving the System of Equations

Adding equations (i) and (ii):

\( (3x - W) + (-x + W) = 200 + 400 \)

Simplifying: \( 2x = 600 \)

Solving for \( x \): \( x = 300 \)

Step 4: Finding the Wage \(W\)

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

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

Simplifying: \( 900 - W = 200 \)

Solving for \( W \): \( W = 700 \)

Conclusion

The employee's wage is 700 rupees.

Was this answer helpful?
0

Top Questions on Profit and Loss

Questions Asked in CAT exam

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
View Solution