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Fixed Wage and Profit Loss Analysis

CAT 2021 Slot 2 · Quantitative Ability · Medium · Profit & Loss

This is a medium Quantitative Ability question from the CAT 2021 Slot 2 paper. It tests Profit & Loss. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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 ₹ 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

Answer

1000

Explanation

Let NN be the total number of pens purchased and WW be the wage of the employee. Cost price of NN pens =8N= 8N. Total cost to Amal =8N+W= 8N + W.

Case 1: Remaining (N−100)(N - 100) pens sold at ₹ 11 each. Total Selling Price =100×12+(N−100)×11=1200+11N−1100=11N+100= 100 \times 12 + (N - 100) \times 11 = 1200 + 11N - 1100 = 11N + 100. Net Profit =(11N+100)−(8N+W)=300  ⟹  3N−W+100=300  ⟹  3N−W=200= (11N + 100) - (8N + W) = 300 \implies 3N - W + 100 = 300 \implies 3N - W = 200.

Case 2: Remaining (N−100)(N - 100) pens sold at ₹ 9 each. Total Selling Price =100×12+(N−100)×9=1200+9N−900=9N+300= 100 \times 12 + (N - 100) \times 9 = 1200 + 9N - 900 = 9N + 300. Net Loss =(8N+W)−(9N+300)=300  ⟹  W−N−300=300  ⟹  W−N=600= (8N + W) - (9N + 300) = 300 \implies W - N - 300 = 300 \implies W - N = 600.

Adding 3N−W=2003N - W = 200 and W−N=600W - N = 600: 2N=800  ⟹  N=4002N = 800 \implies N = 400 Then W=600+400=1000W = 600 + 400 = 1000. The employee's wage is ₹ 1000.

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