Practice MCQ Questions and Answer on Profit and Loss

Solution: Let cost price = 100 × weight 78 = 7800 Sale price = 89 × weight 100 = 8900 Profit % = $$\frac{{1100}}{{7800}}$$  × 100 = 14.1% gain

Solution: Let the marked price be 100 100 == 20% ↓(discount) ⇒ 80 == 10%↓ (discount) ⇒ 72(CP) == 10%↑ (interior) ⇒ 79.2(Total CP) Now, selling price would be 25% above the Total cost price. SP = 79.2 + 25% of 79.2 SP = 99 Now, On comparing, 100 ⇒ 800000 99 ⇒ $$\frac{{800000}}{{100}} \times 99$$    ⇒ 7,92,000 So, SP = Rs. 7,92,000

Solution: $$\eqalign{ & {\text{Initial investment}} \cr & = {\text{Rs}}.8200 \cr & {\text{S}}{\text{.P}}{\text{.of }}{{\text{1}}^{{\text{st}}}}{\text{ term}} \cr & = {\text{Rs}}.\left( {\frac{{125}}{{100}} \times 8200} \right) \cr & = {\text{Rs}}{\text{. }}10250 \cr & {\text{C}}{\text{.P}}{\text{.of }}{{\text{2}}^{{\text{nd}}}}{\text{ term}} \cr & = {\text{Rs}}{\text{. }}10250 \cr & {\text{loss}} = 20\% \cr & {\text{Final receipt}} \cr & = {\text{S}}{\text{.P}}{\text{.of }}{{\text{2}}^{{\text{nd}}}}{\text{ term}} \cr & = {\text{Rs}}.\left( {\frac{{80}}{{100}} \times 10250} \right) \cr & = {\text{Rs}}{\text{. }}8200 \cr} $$ Since initial investment = final receipt, there was neither gain nor loss.

Solution: Cost price of 11 oranges = Rs. 10 Cost price of 1 orange = Rs. $$\frac{{10}}{{11}}$$ Selling price of 10 oranges = Rs. 11 Selling price of 1 orange = Rs. $$\frac{{11}}{{10}}$$ Since Selling price > Cost price, there is profit Profit per orange = Selling price - Cost price $$\eqalign{ & = {\text{Rs}}{\text{.}}\,\frac{{11}}{{10}} - {\text{Rs}}{\text{.}}\,\frac{{10}}{{11}} \cr & = {\text{Rs}}{\text{.}}\,\frac{{121 - 100}}{{110}} \cr & = {\text{Rs}}{\text{.}}\,\frac{{21}}{{110}} \cr} $$ Profit on 11 oranges $$ = \frac{{21}}{{110}} \times 11 = {\text{Rs}}{\text{.}}\,2.1$$ $$\eqalign{ & {\text{Profit}}\% = \frac{{{\text{Profit}}}}{{{\text{Cost}}\,{\text{Price}}}} \times 100\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2.1}}{{10}} \times 100\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 21\% \cr} $$

Solution: In such cases, always loss occurs. It can be calculated by this formula, $$ = \frac{{{{\left( {{\text{loss or gain percentage}}} \right)}^2}}}{{100}} = 4$$ That is 4% of loss Graphic Change method 100 == 20%(loss) ⇒ 120 == 20%(gain) ⇒ 96 % Loss = 4%

Solution: Let the price of 1st item is x Then for 2nd 520 - x Profit and loss of both items are same Then, $$\eqalign{ & \frac{{x \times 16}}{{100}} - \frac{{\left( {520 - x} \right) \times 10}}{{100}} = 0 \cr & \Rightarrow 16x = \left( {520 - x} \right)10 \cr & \Rightarrow 26x = 5200 \cr & \Rightarrow x = 200 \cr & {\text{CP}} = 520 - 200 \cr & \,\,\,\,\,\,\,\,\,\,\, = 320 \cr & {\text{SP}} = 320 \times \frac{{90}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\, = 288 \cr} $$

Solution: Let the C.P. be Rs. 100 Then, Profit = 20% S.P. = Rs. 120 New C.P. = 20% less = Rs. 80 If he gain is 25% then S.P. $$\eqalign{ & = {\text{Rs}}\left( {\frac{{125}}{{100}} \times 80} \right) \cr & = {\text{Rs}}.100 \cr} $$ Difference in S.P. = Rs. (120 - 100) =Rs. 20 If difference in S.P. is Rs. 20, then C.P. = Rs. 100 If difference in S.P. is Rs. 18, then $$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {\frac{{100}}{{20}} \times 18} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}90 \cr} $$

Solution: $$\eqalign{ & {\text{Let}}\,{\text{CP}}\,{\text{of}}\,{\text{whole}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,x \cr & {\text{CP}}\,{\text{of}}\,\frac{1}{2}\,{\text{stock}} = {\text{Rs}}{\text{.}}\,\frac{x}{2} \cr & {\text{CP}}\,{\text{of}}\,\frac{1}{4}\,{\text{stock}} = {\text{Rs}}{\text{.}}\,\frac{x}{4} \cr} $$ $${\text{Total }}\,{\text{SP}}$$ $$ = \,\left[ {\left( {120\% \,{\text{of}}\,\frac{x}{2}} \right) + \left( {80\% \,{\text{of}}\,\frac{x}{4}} \right) + \frac{x}{4}} \right]$$ $$\eqalign{ & = \left( {\frac{{3x}}{5} + \frac{x}{5} + \frac{x}{4}} \right) \cr & = {\text{Rs}}{\text{.}}\,\frac{{21x}}{{20}} \cr & {\text{Gain}} = {\text{Rs}}{\text{.}}\,\left( {\frac{{21x}}{{20}} - x} \right) = {\text{Rs}}{\text{.}}\,\frac{x}{{20}} \cr & \therefore {\text{Gain}}\% = \left( {\frac{x}{{20}} \times \frac{1}{x} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \cr} $$

Solution: 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

Solution: $$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{. be Rs}}{\text{.100}}{\text{.}} \cr & {\text{Then, }} \cr & {\text{marked price = Rs}}{\text{.130}}{\text{.}} \cr & {\text{Selling Price}} \cr & {\text{ = }}\left( {100 - \frac{{25}}{4}} \right)\% {\text{ of Rs}}{\text{.130}} \cr & {\text{ = Rs}}{\text{.}}\left( {\frac{{375}}{{400}} \times 130} \right) \cr & = {\text{Rs}}{\text{.121}}{\text{.875}}{\text{.}} \cr & \therefore {\text{ Profit }}\% \cr & {\text{ = }}\left( {121.875 - 100} \right)\% \cr & {\text{ = 21}}{\text{.875}}\% \cr & {\text{ = }}\frac{{21875}}{{1000}}{\text{ }}\% \cr & {\text{ = 21}}\frac{7}{8}\% \cr} $$