Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

Selling price of potatoes = 25
\[\begin{gathered} \begin{array}{*{20}{c}} {{\text{Cost price}}}&{{\text{Selling price}}} \\ \begin{gathered} 4 \hfill \\ \,\,\,\,\,\,\,\,\, \downarrow \times 5 \hfill \\ 20 \hfill \\ \end{gathered} &\begin{gathered} 5 \hfill \\ \,\,\,\,\,\,\,\,\, \downarrow \times 5 \hfill \\ 25 \hfill \\ \end{gathered} \end{array} \hfill \\ {\text{Profit }}\% = 10\% = \frac{1}{{10}} \hfill \\ \begin{array}{*{20}{c}} {{\text{Cost price}}}&{{\text{Selling price}}} \\ \begin{gathered} 10 \hfill \\ \,\,\,\,\,\,\,\,\, \downarrow \times 2 \hfill \\ 20 \hfill \\ \end{gathered} &\begin{gathered} 11 \hfill \\ \,\,\,\,\,\,\,\,\, \downarrow \times 2 \hfill \\ 22 \hfill \\ \end{gathered} \end{array} \hfill \\ \end{gathered} \]
Selling price of potatoes in evening = Rs. 22

Let 1000 gm price = Rs. 1000
12.5% of 1000 = Rs. 1125
When he gets profit of 12.5% on 1000 gm
$$\eqalign{ & {\text{Then, }}\frac{{1000}}{{1125}} \times 1\,{\text{kg}} \cr & = \frac{{1000 \times 1000{\text{ gm}}}}{{1125}} \cr & = 888.8{\text{ gm}} \cr} $$

∴ (30% of 900) × 3 = Rs. 810

$$\eqalign{ & {\text{Let cost price}} = x \cr & \Rightarrow \frac{{x \times \left( {100 + x} \right)}}{{100}} = 96 \cr & \Rightarrow x \times \left( {100 + x} \right) = 9600 \cr & \Rightarrow x \times \left( {100 + x} \right) = 60 \times \left( {100 + 60} \right) \cr & \Rightarrow x = {\text{Rs}}{\text{. }}60{\text{ Ans}}{\text{.}} \cr} $$

Here, cost price = Rs. 2800, Profit % as selling price = 20
As, according to the question,
Profit as a percentage of selling price $$ = \frac{{{\text{Profit}}}}{{{\text{SP}}}} \times 100$$
$$\eqalign{ & \Rightarrow 20 = \frac{{{\text{Profit}}}}{{{\text{SP}}}} \times 100 \cr & \Rightarrow 20 = \frac{{{\text{SP}} - 2800}}{{{\text{SP}}}} \times 100\,\,\,\,\,\left[ {{\text{As Profit}} = {\text{SP}} - {\text{CP}}} \right] \cr & \Rightarrow 20{\text{SP}} = 100{\text{SP}}\, - 280000 \cr & \Rightarrow 280000 = 80{\text{SP}} \cr & \Rightarrow {\text{SP}} = {\text{Rs}}{\text{. }}3500 \cr} $$
Now,
Actual profit = (SP - CP) = Rs. (3500 - 2800) = Rs. 700
Hence, the actual profit is Rs. 700

17 × C.P. = 8(C.P. + S.P.)
17C.P. = 8C.P. + 8S.P.
9C.P. = 8S.P.
C.P. : S.P. = 8 : 9
Profit = 9 - 8 = 1
Profit % = $$\frac{1}{8}$$ × 100 = 12.5%

Quantity of wheat bought by shopkeeper = 120
Let the price of the 120 quintals of wheat = Rs. 120
According to the question
$$\eqalign{ & 120 \times \frac{1}{5} \times \frac{{75}}{{100}} + 120 \times \frac{4}{5} \times \frac{{100 + x}}{{100}} = 120 \times \frac{{125}}{{100}} \cr & \Rightarrow 18 + \frac{{24}}{{25}} \times \left( {100 + x} \right) = 150 \cr & \Rightarrow \frac{{24}}{{25}} \times \left( {100 + x} \right) = 150 - 18 \cr & \Rightarrow \frac{{24}}{{25}} \times \left( {100 + x} \right) = 132 \cr & \Rightarrow 100 + x = 132 \times \frac{{25}}{{24}} \cr & \Rightarrow 100 + x = 137.5 \cr & \Rightarrow x = 137.5 - 100 \cr & \Rightarrow x = 37.5\% {\text{ or }}37\frac{1}{2}\% \cr} $$

$$\eqalign{ & 355 \times \frac{{100}}{{71}} = {\text{Cost price}} \cr & {\text{Sale price}} = 355 \times \frac{{100}}{{71}} \times \frac{{121}}{{100}} = 605 \cr} $$

$$\eqalign{ & \frac{{{\text{Sale Price}}}}{{{\text{Cost Price}}}} = \frac{{20}}{{23}} \times \frac{{1000}}{{800}} = \frac{{50}}{{46}} \cr & {\text{Cost Price}} = 46 \cr & {\text{Sale Price}} = 50 \cr & {\text{Profit }}\% = \frac{4}{{46}} \times 100 = 8\frac{{16}}{{23}}\% \cr} $$

As, Loss (a) = 7% and Less weight (b) = 18%
Then,
$$\eqalign{ & \frac{{{\text{Profit }}\% }}{{{\text{Loss }}\% }} = \frac{{{\text{b}} \pm {\text{a}}}}{{100 - {\text{b}}}} \times 100 \cr & \Rightarrow \frac{{18 - 7}}{{100 - 18}} \times 100 \cr & \Rightarrow \frac{{11}}{{82}} \times 100 \cr & \Rightarrow 13.4146 \approx 13.41\% \cr} $$
∴ The dealer's profit % is 13.41%.