Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

Let cost price of hand cart = 100
According to the question,
\[{\text{100 (cp)}}\xrightarrow{{25\% {\text{Loss}}}}75{\text{ }}({\text{sp}})\xrightarrow{{ \times \frac{{48}}{5}}}720\,{\text{(given)}}\]
$$\eqalign{ & 75\,{\text{units}} \to 720 \cr & 1\,{\text{unit}} \to \frac{{720}}{{75}} = \frac{{48}}{5} \cr & 100\,{\text{units}} \to \frac{{48}}{5} \times 100 = 960 \cr & \therefore {\text{Cost price}} = {\text{ Rs}}{\text{.960}} \cr & {\text{To gain }}25\% {\text{ selling price is }} \cr & = {\text{cp}} + {\text{profit}}\% \times {\text{cp}} \cr & = 960 + \frac{{25}}{{100}} \times 960 \cr & = 960 + 240 = {\text{Rs}}{\text{.}}\,1200 \cr} $$

According to the question,
Cheats while buying = 10%
Cheats while selling = 10%
$$\eqalign{ & \therefore \left( {a + b + \frac{{ab}}{{100}}} \right)\% \cr & = 10 + 10 + \frac{{10 \times 10}}{{100}} \cr & = 20 + 1 \cr & = 21 \cr} $$
∴ Increase in profit % = 21%

Given loss = 10% profit = 10%
Difference of overall profit and loss = 10 - (-10) = 20%
20% of cp = sp
$$\frac{{20}}{{100}} \times {\text{cp = 108}}$$
20 × cp = 108 × 100
cp = $$\frac{{10800}}{{20}}$$
∴ cp = 540

$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\,x. \cr & {\text{Then,}} \cr & {\text{S}}{\text{.P}}{\text{.}} = 110\% {\text{ of Rs}}.\,x. \cr & = {\text{Rs}}.\frac{{11x}}{{10}} \cr & {\text{New S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {2 \times \frac{{11x}}{{10}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{11x}}{5} \cr & {\text{Gain}} = {\text{Rs}}.\left( {\frac{{11x}}{5} - x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{6x}}{5} \cr & \therefore {\text{Gain}}\% = \left( {\frac{{6x}}{5} \times \frac{1}{x} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 120\% \cr} $$

$$\eqalign{ & {\text{Let S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\,x \cr & {\text{Then,}} \cr & {\text{Loss}} = {\text{Rs}}.\frac{x}{3} \cr & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {x + \frac{x}{3}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{4x}}{3} \cr & \therefore {\text{Loss }}\% \cr & = \left( {\frac{x}{3} \times \frac{3}{{4x}} \times 100} \right)\% \cr & = 25\% \cr} $$

Let C.P. = Rs. x
Then, 1754 - x = x - 1492
⇒ 2x = 3246
⇒ x = 1623

Let first radio CP is x second radio CP is 1920 - x
As is given,
$$x \times \frac{{\left( {100 + 20} \right)}}{{100}} = \left( {1920 - x} \right) \times $$      $$\frac{{\left( {100 - \frac{{20}}{3}} \right)}}{{100}}$$
$$\eqalign{ & 120 \times x = \left( {1920 - x} \right) \times \left( {\frac{{280}}{3}} \right) \cr & 360 \times x = \left( {1920 - x} \right) \times 280 \cr & 640 \times x = 1920 \times 28 \cr & \therefore x = 840 \cr} $$
Hence, second radio cp is 1920 - x
= 1920 - 840
= 1080
CP of both Radio = 840 and 1080

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{cost}}\,{\text{price}}\,{\text{be}}\,x \cr & {\text{gain}} = 5\% \cr & {\text{Selling}}\,{\text{Price}} = \frac{{105x}}{{100}} \cr & {\text{New}}\,{\text{SP}} = \frac{{105x}}{{100}} - 12 \cr & {\text{Now}}\,{\text{there}}\,{\text{is}}\,{\text{a}}\,{\text{loss}}\,{\text{of}}\,2.5\% \cr & x \times \frac{{100 - 2.5}}{{100}} = \frac{{105x}}{{100}} - 12 \cr & \frac{{97.5x}}{{100}} = \frac{{105x}}{{100}} - 12 \cr & 97.5x = 105x - 1200 \cr & 7.5x = 1200 \cr & \therefore x = 160 \cr} $$

Let the CP₁ of article = 100x
Initial SP₁ = 100x + 12% of 100x = 100x + 12x = 112x
Now, If He brought article at 10% discount. Therefore CP₂ = 90x
Now SP₂ = 90x + 30% of 90x = 90x + 27x =117x
According to question
SP₂ - SP₁ = 5.75
⇒ 117x - 112x = 5.75
⇒ 5x = 5.75
⇒ x = $$\frac{5.75}{5}$$
⇒ x = 1.15
Initial Cost of article = 100 × 1.15 = Rs. 115
To sold article at 20% profit
= 115 + 20% of 115
= 115 + 23
= Rs. 138

$$\eqalign{ & {\text{S}}{\text{.P}}{\text{. of 90 ball pens}} \cr & = {\text{Rs}}{\text{. 160, loss}} = 20\% \cr & {\text{C}}{\text{.P}}{\text{.of 90 ball pens}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{80}} \times 160} \right) \cr & = {\text{Rs}}{\text{. }}200 \cr} $$
∴ Desired S.P. of 90 ball pens
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{{120}}{{100}} \times 200} \right) \cr & = {\text{Rs}}{\text{. }}240 \cr} $$
For Rs. 240, ball pens sold = 90
For Rs. 96, ball pens sold
$$\eqalign{ & = \left( {\frac{{90}}{{240}} \times 96} \right) \cr & = 36 \cr} $$