CAT 2021 Set-1 | Quantitative Aptitude | Question: 9

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 $₹ \; 11$ 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 $\text{INR},$ is

Answer 1

Let the number of pens purchased be $`x\text{’}.$ Then his cost price be ₹$8x$ for the pens.

 Let us assume the fixed wages to be ₹ $\text{W}.$ Then his net cost price will be ₹$(8x+\text{W}).$

Now, The total selling price $\text{TSP1}= 12 \times 100 + (x-100) \times 11 = 1200 + 11x-1100$

$\qquad \qquad \qquad \qquad \qquad = 11x+100\; \longrightarrow (1)$

And, the total selling price $\text{TSP2}= 12 \times 100 + (x-100) \times 9 = 1200 + 9x-900$

$\qquad \qquad \qquad \qquad \qquad =9x+300\; \longrightarrow (2)$

Now, $11x+100 = 8x+\text{W}+300$

$\Rightarrow 3x - \text{W} = 200\; \longrightarrow (3)$

And, $9x + 300 = 8x + \text{W} – 300$

$\Rightarrow x - \text{W} = -600\; \longrightarrow (4)$

On Subtract the equations $(3)$ and $(4).$

$\begin{array}{} 3x – \text{W} = 200 \\ x – \text{W} = -600 \\ –  \;\; + \qquad \; + \\\hline  2x = 800 \end{array}$

$\Rightarrow  \boxed{x = 400}$

Put the value of $x$ in equation $(4).$

$\Rightarrow 400 – \text{W} = -600$

$\Rightarrow\boxed{\text{W} = ₹1000}$

$\therefore$ The wage of the employee, in INR is ₹$1000.$

Correct Answer $: 1000$