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CAT 2021 Slot 1 — QA Question 2

Profit & LossEasy

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 & solution

Answer: 1000

Solution

Easy

Let the total pens be xx and the wage be ww. Cost =8x+w=8x+w. Revenue is fixed for the first 100 pens; the two selling-price scenarios give two linear equations in xx and ww — solve them.

1

Cost and the first 100 pens. Cost price is 88 per pen plus the fixed wage; the first 100100 pens fetch \unicodex20B912\unicode{x20B9}12 each.

Cost=8x+wRevenue from first 100=100×12=1200\begin{aligned} &\text{Cost}=8x+w\\ &\text{Revenue from first 100}=100\times 12=1200 \end{aligned}
2

Case 1 — remaining sold at \unicodex20B911\unicode{x20B9}11, net profit 300300. The remaining (x−100)(x-100) pens sell at 1111 each, and revenue exceeds cost by 300300.

1200+11(x−100)=8x+w+300⇒ 1200+11x−1100=8x+w+300⇒ 3x−200=w...(1)\begin{aligned} &1200+11(x-100)=8x+w+300\\ &\Rightarrow\ 1200+11x-1100=8x+w+300\\ &\Rightarrow\ 3x-200=w \quad\text{...(1)} \end{aligned}
3

Case 2 — remaining sold at \unicodex20B99\unicode{x20B9}9, net loss 300300. Now revenue falls short of cost by 300300.

1200+9(x−100)=8x+w−300⇒ 1200+9x−900=8x+w−300⇒ x+600=w...(2)\begin{aligned} &1200+9(x-100)=8x+w-300\\ &\Rightarrow\ 1200+9x-900=8x+w-300\\ &\Rightarrow\ x+600=w \quad\text{...(2)} \end{aligned}
4

Solve (1) and (2). Equate the two expressions for ww.

3x−200=x+600[(1)=(2)]⇒ 2x=800⇒x=400⇒ w=x+600=400+600=1000(from (2))\begin{aligned} &3x-200=x+600 \quad\text{[(1)=(2)]}\\ &\Rightarrow\ 2x=800 \Rightarrow x=400\\ &\Rightarrow\ w=x+600=400+600=1000 \quad\text{(from (2))} \end{aligned}
Wage of the employee=\unicodex20B9 1000\text{Wage of the employee}=\unicode{x20B9}\,1000