Profit and Loss Question 2 - CAT 2021
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 ₹ 11 each, 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:
Step-by-Step Explanation
Let the total number of pens purchased be n.
Total Cost Incurred: CP = 8n + W, where W is the employee's fixed wage.
Now evaluate the two selling scenarios for the remaining n − 100 pens:
- Scenario 1 (Remaining sold at ₹ 11):
Total SP₁ = 100 × 12 + 11(n − 100) = 1200 + 11n − 1100 = 11n + 100
Profit = SP₁ − CP = 300
11n + 100 − 8n − W = 300
3n − W = 200 --- (Equation 1)
- Scenario 2 (Remaining sold at ₹ 9):
Total SP₂ = 100 × 12 + 9(n − 100) = 1200 + 9n − 900 = 9n + 300
Loss = CP − SP₂ = 300
8n + W − 9n − 300 = 300
W − n = 600 --- (Equation 2)
Add Equation 1 and Equation 2 together to eliminate W:
(3n − W) + (W − n) = 200 + 600
2n = 800
n = 400 pens
Substitute n = 400 back into Equation 2 to find the wage:
W − 400 = 600
W = 1000
The fixed wage of the employee is ₹ 1000.
Correct Answer: 1000
💡 FundaMakers Tip:
Look at the variance between the two situations. The cost price structure and the first 100 pens sold are completely identical in both cases. The only difference is that the remaining pens are sold for ₹ 11 instead of ₹ 9—a difference of ₹ 2 per pen.
This change shifts the merchant's final position from a ₹ 300 profit to a ₹ 300 loss—a net variance of ₹ 600.
Remaining Pens × 2 = 600
Remaining Pens = 300
Total pens n = 300 + 100 = 400.
Analyzing the delta saves you from writing out full algebraic setups.