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
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: Jul 27, 2024
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Correct Answer: 700
Solution and Explanation
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.
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