Management Aptitude Test 2016 Paper

(d) Let number of CDs bought be x.
Given, CP = ₹ 1800
Then, CP of each CD = ₹ $\frac{1800}{\mathit{x}}$
It is given that the man sold (x - 1) CDs at a profit of ₹ 6 each.
Now, SP = ₹ $\left(\frac{1800}{\mathit{x}}+6\right)$ (x - 1)
∴ Profit = SP - CP
⇒ 114 = $\left(\frac{1800}{\mathit{x}}+6\right)$ (x - 1) - 1800
⇒ 114 = $\frac{\left(1800+6\mathit{x}\right)\left(\mathit{x}-1\right)-1800\mathit{x}}{\mathit{x}}$
⇒ 114x = 1800x + 6 ${\mathit{x}}^2$ - 1800 - 6x - 1800x
⇒ 114 = 6 ${\mathit{x}}^2$ - 6x - 1800
⇒ 6 ${\mathit{x}}^2$ - 120x - 1800 = 0
⇒ x = $\frac{120\pm \sqrt{{\left(120\right)}^2+4\times 6\times 1800}}{12}$
= $\frac{120\pm \sqrt{14400+43200}}{12}$
= $\frac{120\pm 240}{12}=\frac{360}{12}$ = 30
Hence, total number of CDs bought is 30.