Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{Let the S}}{\text{.P}}{\text{. be Rs}}{\text{. }}x. \cr & {\text{Then,}} \cr & = x - 10\% {\text{ of }}x = 27 \cr & \Leftrightarrow 90\% {\text{ of }}x = 27 \cr & \Leftrightarrow x = \left( {27 \times \frac{{10}}{9}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 30 \cr} $$

$$\eqalign{ & {\text{Let the S}}{\text{.P}}{\text{. be Rs}}{\text{. }}x. \cr & {\text{Profit}} = 25\% \cr & {\text{Then,}} \cr & {\text{C}}{\text{.P}}{\text{.}} = x - 25\% {\text{ of Rs}}{\text{. }}x \cr & = 75\% {\text{ of Rs}}{\text{. }}x \cr & = {\text{Rs}}{\text{.}}\left( {\frac{3}{4}x} \right) \cr & {\text{Profit}} = {\text{Rs}}.\left( {x - \frac{3}{4}x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{x}{4} \cr & \therefore {\text{Profit }}\% \cr & = \left( {\frac{x}{4} \times \frac{4}{{3x}} \times 100} \right)\% \cr & = 33\frac{1}{3}\% \cr} $$

$$\eqalign{ & 5\% = \frac{{1 \leftarrow {\text{Discount}}}}{{20 \leftarrow {\text{Marked price}}}} \cr & {\text{So, Selling price}} = 19 \cr & \,\,\,\,\,{\text{MP}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{SP}} \cr & \mathop { \downarrow \times 50}\limits_{1000}^{20} \,\,\,\,\,\mathop {\,\,\,\,\,\,\,\,\,\, \downarrow \times 50}\limits_{950}^{19} \cr} $$

let the Marked price of product = 900
∴ cost price will be = 900 × $$\frac{5}{9}$$ = 500
Profit = 20%
Selling price will be = 500 + 20% of 500 = 600
Discounted value = 900 - 600 = 300
Discount % = $$\frac{{100 \times 300}}{{900}} = 33\frac{1}{3}\% $$

Let the CP₁ of Product= 300
Initial SP₁ = 300 + $$33\frac{1}{3}$$% of 300 = 300 + 100 = 400
Now, If cost of the production goes up by 12%.
∴ CP₂ = 300 + 12% of 300 = 300 + 36 = 336
Now SP₂ = 400 + 10% of 400 = 400 + 40 = 440
Profit = 440 - 336 = 104
Profit % $$ = \frac{{104}}{{336}} \times 100 = 30\frac{{20}}{{21}}\% $$

$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{. be Rs}}{\text{. }}x. \cr & {\text{Then,}} \cr & {\text{Profit}} = 20\% {\text{ of Rs}}{\text{. }}x \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{x}{5} \cr & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {x + \frac{x}{5}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{6x}}{5} \cr & \therefore {\text{Desired profit }}\% \cr & = \left( {\frac{x}{5} \times \frac{5}{{6x}} \times 100} \right)\% \cr & = 16\frac{2}{3}\% \cr} $$

Let,
C.P. = Rs. x,
Profit% = x% and
S.P. = Rs. 144
$$\eqalign{ & \therefore x = \left[ {\frac{{100}}{{\left( {100 + x} \right)}} \times 144} \right] \cr & \Rightarrow {x^2} + 100x = 14400 \cr & \Rightarrow {x^2} + 100x - 14400 = 0 \cr & \Rightarrow {x^2} + 180x - 80x - 14400 = 0 \cr & \Rightarrow \left( {x + 180} \right)\left( {x - 80} \right) = 0 \cr & \Rightarrow x = 80 \cr} $$

Marked Price = 250
Selling Price= 225
Difference = 250 - 225 = 25
Discount = $$\frac{{25}}{{250}} \times 100 = 10\% $$

$$\eqalign{ & {\text{Discount}} = x\% \cr & \Rightarrow {\text{Selling price}} = {\text{Rs}}{\text{.}}y \cr & \Rightarrow {\text{MRP}} = ? \cr & \Rightarrow {\text{MRP}} \times \left( {100 - x} \right)\% = y \cr & \Rightarrow {\text{MRP}} = \frac{y}{{\left( {100 - x} \right) \times \frac{1}{{100}}}} \cr & \Rightarrow {\text{MRP}} = {\text{Rs}}.\frac{{100y}}{{\left( {100 - x} \right)}} \cr} $$

$$\eqalign{ & {\text{CP}} = {\text{100 }} - {\text{ D% }} \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{100 }} - {\text{ 10}} \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{90}} \cr & {\text{MP}} = {\text{100 + P% }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{100 + 26}} \cr & \,\,\,\,\,\,\,\,\,\,\,{\text{ = 126}} \cr & {\text{Difference = 126 }} - {\text{ 90}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 36}} \cr & {\text{Required }}\% = \frac{{36}}{{90}} \times 100 = 40\% \cr} $$