Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

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

$$\eqalign{ & {\text{Cost Price}} = \frac{{350}}{{100}} = 3.50 \cr & {\text{Sale Price}} = \frac{{48}}{{12}} = 4 \cr & {\text{Profit}} = 0.50 \cr & {\text{Profit }}\% = \frac{{0.50}}{{3.50}} \times 100 = \frac{{100}}{7} = 14\frac{2}{7}\% \cr} $$

$$33\frac{1}{3}\% = \frac{1}{3}$$
Let, selling price = 90
Let, SP = 3 × 3 = multiple of 9
SP₁ = $$\frac{1}{3}$$ × 90 = 30
(Cost price) = (Selling price) $$\left[ {\frac{{100}}{{100 - {\text{loss}}\% }}} \right]$$
= 30 × $$\frac{3}{2}$$
= 45
Original selling price 80% of
SP₂ = $$\frac{{80}}{{100}}$$ × 90 = 72
Profit = 72 - 45 = 27
Profit % = $$\frac{{27}}{{45}}$$ × 100 = 60%

Cost price of 1 kg potato = 18
Selling price of 1 kg potato = 22
Profit % $$ = \frac{4}{{18}} \times 100 = 22.22\% $$
Now,

Let 36 gm weight cost price = Rs. 80
1 gm weight cost price = $$ = \frac{{80}}{{36}} = \frac{{20}}{9}$$
28 gm weight selling price = Rs. 70
28 gm weight selling price $$ = \frac{{70}}{{28}} = \frac{5}{2}$$
Profit $$ = \frac{5}{2} - \frac{{20}}{9} = \frac{5}{{18}}$$
Profit % $$ = \frac{{5 \times 9}}{{18 \times 20}} \times 100 = \frac{{25}}{2} = 12.5\% $$

$$\eqalign{ & {\bf{Alternate}}\,{\bf{solution:}} \cr & 12.5\% = \frac{1}{8} \cr & \frac{{{\text{Selling price}}}}{{{\text{Cost price}}}} = \frac{7}{8} \times \frac{{36}}{{28}} = \left. {\frac{9}{8}} \right)1\,{\text{Profit}} \cr & {\text{Profit }}\% = \frac{1}{8} \times 100 = 12.5\% \cr} $$

Hence, 8x × $$\frac{7}{5}$$ = 11x + 1000
56x = 55x + 5000
x = 5000
Hence, cost price = 10x
= 10 × 5000
= 50000 Answer

$$18\% \to \frac{9}{{50}}$$
59 unit → Rs. 53.10
1 unit → Rs. 0.9
50 unit → 9 × 5 = Rs. 45

$$\eqalign{ & {\bf{Given:}} \cr & \frac{{{\text{CP}} - {\text{SP}}}}{{{\text{CP}}}} \times 100 = 25 - - - \left( 1 \right) \cr & \frac{{{\text{SP}} + 660 - 2{\text{CP}}}}{{2{\text{CP}}}} \times 100 = 20 - - - \left( 2 \right) \cr & {\bf{Formula}}\,{\bf{used:}} \cr & {\text{Profit }}\% = \frac{{{\text{Profit}}}}{{{\text{CP}}}} \times 100 \cr & {\text{Loss }}\% = \frac{{{\text{Loss}}}}{{{\text{CP}}}} \times 100 \cr & {\text{Profit}} = {\text{SP}} - {\text{CP}} \cr & {\text{Loss}} = {\text{CP}} - {\text{SP}} \cr & {\text{CP}} = {\text{Cost price}} \cr & {\text{SP}} = {\text{Selling price}} \cr & {\bf{Solution:}} \cr & {\text{Let's solve the first equation,}} \cr & 1 - \frac{{{\text{SP}}}}{{{\text{CP}}}} = 0.25 \cr & \frac{{{\text{SP}}}}{{{\text{CP}}}} = 0.75 \cr & {\text{SP}} = 0.75{\text{CP}} \cr & {\text{Now, let's put the value of SP in the second equation,}} \cr & \frac{{0.75{\text{CP}} + 660 - 2{\text{CP}}}}{{2{\text{CP}}}} \times 100 = 20 \cr & \frac{{660 - 1.25{\text{CP}}}}{{2{\text{CP}}}} = 0.2 \cr & 660 - 1.25{\text{CP}} = 0.4{\text{CP}} \cr & {\text{CP}} = \frac{{660}}{{1.65}} \cr & {\text{CP}} = 400 \cr & {\text{The original cost price is Rs}}{\text{. 400}} \cr} $$

Selling price of 800 g goods with 20% profit $$ = \frac{{1000\left( {100 + 20} \right)}}{{100}} = {\text{Rs}}{\text{. }}1200$$
Cost price of 800 g goods = Rs. 800
Gain = Selling price - Cost price = 1200 - 800 = 400
$$\eqalign{ & {\text{Gain }}\% = \frac{{400}}{{800}} \times 100\% \cr & = \left( {0.5 \times 100} \right)\% \cr & = 50\% \cr} $$
∴ His real gain percentage is 50%

Investments = 200 : 300
\[\begin{array}{*{20}{c}} {200}&:&{300} \\ {\,\,\,\,\,\,\,\,\,\, \downarrow + 10\% }&{}&{\,\,\,\,\,\,\,\,\,\, \downarrow - 20\% } \\ {220}&{}&{240} \end{array}\]
Investments = 500
After increase/decrease = 460
Loss = 40
Loss % = $$\frac{{40}}{{500}}$$ × 100 = 8%