Subject: General Aptitude · Chapter: Profit and Loss · Exam: · Marks: · Difficulty:
If a shopkeeper sells $\frac{1}{3}$ of his goods at a profit of $14 \%, \frac{3}{5}$ of the goods at a profit of 17.5\% and the remaining at a profit of 20\%, then his profit on the whole is equal to
(a)15.5\%
(b)16\%
(c)16.5\%
(d)17\%
Answer
Answer (as printed): C
Explanation
Let the C.P. of whole be ₹ $x$. Then, C.P. of $\frac{1}{3} \mathrm{rd}$ goods $=₹ \frac{x}{3}$, C.P. of $\frac{3}{5}$ th goods $=₹ \frac{3 x}{5}$. C.P. of remaining goods $=₹\left[x-\left(\frac{x}{3}+\frac{3 x}{5}\right)\right]=₹ \frac{x}{15}$. $$\begin{aligned} \text { Total S.P. } & =₹\left(114 \% \text { of } \frac{x}{3}+117 \frac{1}{2} \% \text { of } \frac{3 x}{5}+120 \% \text { of } \frac{x}{15}\right) \\ = & ₹\left(\frac{38 x}{100}+\frac{141 x}{200}+\frac{8 x}{100}\right)=₹\left(\frac{233 x}{200}\right) . \\ \text { Profit }=₹ & \left(\frac{233 x}{200}-x\right)=₹ \frac{33 x}{200} . \\ \therefore \text { Profit } \% & =\left(\frac{33 x}{200} \times \frac{1}{x} \times 100\right) \%=\frac{33}{2} \%=16.5 \% . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.