Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{Profit}}\% = 25 \cr & 25\% = \frac{1}{4} \cr & {\text{CP}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{SP}} \cr & \,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5 \cr & \,\,\,\,1 - - - 210 \cr & \therefore {\text{SP}} = 210 \times 5 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1050 \cr} $$

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Alternate Solution :
Let Cost price is 100x
Then Selling price is 125x
According to the question,
Selling price - Cost Price = 210
⇒ 125x - 100x = 210
⇒ x = $$\eqalign{ \frac{210}{25} \cr }$$
So the Selling price → 125x
= 125 × $$\eqalign{ \frac{210}{25} \cr }$$
= Rs. 1050

Let the initial SP = 100
After reducing 60% SP = 100 - 60 = 40
According to the question if the product is sold on 40 there is a loss of 10%.
Then CP = $$\frac{{40}}{{90}} \times 100 = \frac{{400}}{9}$$
Profit = $$100 - \frac{{400}}{9} = \frac{{500}}{9}$$
∴ Profit % = $$\frac{{\frac{{500}}{9}}}{{\frac{{400}}{9}}} \times 100 = 125\% $$

According to the question,
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{.}} = \frac{{95}}{{100}}{\text{S}}{\text{.P}}{\text{.}} \cr & \frac{{{\text{C}}{\text{.P}}}}{{{\text{S}}{\text{.P}}{\text{.}}}}{\text{ = }}\frac{{95}}{{100}}{\text{ = }}\left. {\frac{{19}}{{20}}} \right\rangle {\text{1 unit profit}} \cr & {\text{Profit }}\% = \frac{1}{{19}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5.26\% {\text{ }} \cr} $$

Let marked price be Rs. 100
Then,
S.P. = 85% of 88% of 90% of Rs. 100
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{85}}{{100}} \times \frac{{88}}{{100}} \times \frac{{90}}{{100}} \times 100} \right) \cr & = {\text{Rs}}.67.32 \cr} $$
∴ Single Discount
= (100 - 67.32)%
= 32.68%

Let marked price be Rs. 100
Then,
S.P. = (100 - q)% of (100 - p)% of Rs. 100
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left[ {\frac{{100 - {\text{q}}}}{{100}} \times \frac{{100 - {\text{p}}}}{{100}} \times 100} \right] \cr & = {\text{Rs}}.\left[ {\frac{{\left( {100 - {\text{q}}} \right)\left( {100 - {\text{p}}} \right)}}{{100}}} \right] \cr & \therefore {\text{Single discount }} \cr & = \left\{ {100 - \left[ {\frac{{\left( {100 - {\text{q}}} \right)\left( {100 - {\text{p}}} \right)}}{{100}}} \right]} \right\}\% \cr & = \left( {{\text{p}} + {\text{q}} - \frac{{{\text{pq}}}}{{100}}} \right)\% \cr} $$

According to the question,
$$\eqalign{ & {\text{C}}{\text{.P}}{\text{. = }}\frac{{90}}{{100}}{\text{S}}{\text{.P}}{\text{.}} \cr & \frac{{{\text{C}}{\text{.P}}{\text{.}}}}{{{\text{S}}{\text{.P}}{\text{.}}}}{\text{ = }}\left. {\frac{9}{{10}}} \right\rangle {\text{1 unit profit}} \cr & {\text{Profit }}\% = \frac{1}{9} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\frac{1}{9}\% {\text{ }} \cr} $$

Let the cost price is x
According to question
$$\eqalign{ & \Rightarrow x \times \frac{{100 + 30}}{{100}} = 1690 \cr & \Rightarrow x \times \frac{{130}}{{100}} = 1690 \cr & \therefore x = \frac{{1690 \times 100}}{{130}} \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,1300 \cr} $$

$$\eqalign{ & {\text{Real}}\,{\text{Price}} = 100 \cr & {\text{CP}} = 95 \cr & {\text{SP}} = 95 \times \frac{{120}}{{100}} \cr & \,\,\,\,\,\,\,\,\, = 114 \cr & \therefore {\text{Profit}}\% = 14\% \cr} $$

S.P. = 88% of 90% of Rs. 250
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{{88}}{{100}} \times \frac{{90}}{{100}} \times 250} \right) \cr & = {\text{Rs}}.198 \cr} $$

S.P. = 95% of 95% of Rs. 80
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{{95}}{{100}} \times \frac{{95}}{{100}} \times 80} \right) \cr & = {\text{Rs}}.72.20 \cr} $$