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Amal purchases some pens at ₹ 88 each. To sell these, he hires an employee at a fixed wage. He sells 100100 of these pens at ₹12₹ 12 each. If the remaining pens are sold at ₹11₹ 11 each, then he makes a net profit of ₹ 300300, while he makes a net loss of ₹ 300300 if the remaining pens are sold at ₹ 99 each. The wage of the employee, in INR, is

Entered answer:

Solution

✅ Correct Answer: 1000

Let us define the variables for this profit-loss problem:

nn = total number of pens Amal purchased

kk = fixed wage of the employee (what we need to find)

Cost price per pen = ₹8

Total cost = Cost of pens + Employee wage = 8n+k8n + k


Amal has a specific selling strategy:

First 100 pens: sold at ₹12 each

Remaining pens: sold at different prices in two scenarios

Revenue from first 100 pens = 100×12=₹1200100 \times 12 = ₹1200 (same in both scenarios)

Remaining pens = (n−100)(n - 100)


For the first scenario where remaining pens are sold at ₹11 each with net profit ₹300:

Total Revenue = 1200+(n−100)×111200 + (n - 100) \times 11

Using the profit formula Revenue - Total Cost = Profit:

[1200+(n−100)×11]−[8n+k]=300[1200 + (n - 100) \times 11] - [8n + k] = 300

1200+11n−1100−8n−k=3001200 + 11n - 1100 - 8n - k = 300

100+3n−k=300100 + 3n - k = 300

3n−k=2003n - k = 200 ... (Equation 1)


For the second scenario where remaining pens are sold at ₹9 each with net loss ₹300:

Total Revenue = 1200+(n−100)×91200 + (n - 100) \times 9

Using the loss formula Total Cost - Revenue = Loss:

[8n+k]−[1200+(n−100)×9]=300[8n + k] - [1200 + (n - 100) \times 9] = 300

8n+k−1200−9n+900=3008n + k - 1200 - 9n + 900 = 300

−n+k−300=300-n + k - 300 = 300

n−k=−600n - k = -600 ... (Equation 2)


From Equation 1: 3n−k=2003n - k = 200

From Equation 2: n−k=−600n - k = -600

Subtracting Equation 2 from Equation 1:

(3n−k)−(n−k)=200−(−600)(3n - k) - (n - k) = 200 - (-600)

2n=8002n = 800

n=400n = 400


Substituting n=400n = 400 into Equation 2:

400−k=−600400 - k = -600

k=1000k = 1000


This problem demonstrates how profit/loss scenarios create a system of equations. When we have two unknowns and two different outcomes, we can set up equations based on Revenue - Cost = Profit (or Loss) and solve them simultaneously.

Therefore, the wage of the employee is ₹1000.

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