Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

Let the CP of horse = Rs. x
Then, CP of second horse = Rs. (19500 - x)
According to the question,
$$\eqalign{ & x \times \frac{{80}}{{100}} = \left( {19500 - x} \right) \times \frac{{115}}{{100}} \cr & \Rightarrow 16x = 23\left( {19500 - x} \right) \cr & \Rightarrow 16x = 448500 - 23x \cr & \Rightarrow 39x = 448500 \cr & \Rightarrow x = \frac{{448500}}{{39}} \cr & \Rightarrow x = {\text{Rs}}{\text{.}}\,11500 \cr} $$
∴ CP of first horse = Rs. 11500
∴ CP of second horse
= Rs. 19500 - 11500
= Rs. 8000

$$\eqalign{ & {\text{Total Selling Price}} \cr & = {\text{Rs}}{\text{.}}\left( {2 \times 99} \right) \cr & = {\text{Rs}}.198 \cr & {\text{C}}{\text{.P}}{\text{. of first article}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{110}} \times 99} \right) \cr & = {\text{Rs}}{\text{. }}90 \cr & {\text{C}}{\text{.P}}{\text{. of second article}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{90}} \times 99} \right) \cr & = {\text{Rs}}{\text{. }}110 \cr & {\text{Total C}}{\text{.P}}{\text{.}} \cr & = {\text{Rs}}.\left( {90 + 110} \right) \cr & = {\text{Rs}}{\text{. }}200 \cr & \therefore {\text{Loss}} = {\text{Rs}}.\left( {200 - 198} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}2 \cr} $$

$$\eqalign{ & {\text{Total Selling Price}} \cr & = {\text{Rs}}.\left( {2 \times 500} \right) \cr & = {\text{Rs}}{\text{. }}1000 \cr & {\text{C}}{\text{.P}}{\text{. of first chair}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{120}} \times 500} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{1250}}{3} \cr & {\text{C}}{\text{.P}}{\text{. of Second chair}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{88}} \times 500} \right) \cr & = {\text{Rs}}.\frac{{6250}}{{11}} \cr & {\text{Total C}}{\text{.P}}{\text{.}} \cr & = {\text{Rs}}.\left( {\frac{{1250}}{3} + \frac{{6250}}{{11}}} \right) \cr & = {\text{Rs}}.\left( {\frac{{32500}}{{33}}} \right) \cr & {\text{Gain}} = {\text{Rs}}.\left( {1000 - \frac{{32500}}{{33}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\left( {\frac{{500}}{{33}}} \right) \cr & \therefore {\text{Gain }}\% \cr & = \left( {\frac{{500}}{{33}} \times \frac{{33}}{{32500}} \times 100} \right)\% \cr & = 1.54\% \approx 1.5\% \cr} $$

Total C.P. = Rs. (120 × 110) = Rs. 13200
Total S.P.
= Rs. [(30 × 110 + 30 × 12) + (75 × 110 + 75 × 14) + (15 × 110 - 15 × 7)]
= Rs. 14505
$$\eqalign{ & {\text{Average profit }} \cr & {\text{ = Rs}}{\text{.}}\left( {\frac{{14505 - 13200}}{{120}}} \right) \cr & = {\text{Rs}}.\frac{{1305}}{{120}} \cr & = {\text{Rs}}.10.875 \cr} $$

Total SP = Rs. 8000 and Total CP = Rs. 8000
SP of 1^st articles = Rs. 4000
Gain on it = 25%
∴ CP of 1^st articles $$ = {\text{Rs}}{\text{.}}\,\left( {\frac{{100}}{{125}} \times 4000} \right) = {\text{Rs}}{\text{.}}\,3200$$
∴ CP of 2^nd articles = Rs. (8000 - 3200) = Rs. 4800
SP of 2^nd articles = Rs. 4000
∴ Loss on 2^nd articles
$$\eqalign{ & = \left( {\frac{{800}}{{4800}} \times 100} \right)\% \cr & = 16\frac{2}{3}\% \cr} $$

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 $$ = \frac{{21}}{{110}} \times 11 = {\text{Rs}}{\text{.}}\,2.1$$
$$\eqalign{ & {\text{Profit}}\% = \frac{{{\text{Profit}}}}{{{\text{Cost}}\,{\text{Price}}}} \times 100\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2.1}}{{10}} \times 100\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 21\% \cr} $$

let the person buy 10 articles.
Total CP $$ = {\text{Rs}}{\text{.}}\,\left( {1 + \frac{5}{4}} \right) = {\text{Rs}}{\text{.}}\,\frac{9}{4}$$
SP of 10 articles
$$\eqalign{ & = {\text{Rs}}{\text{.}}\,\frac{2}{9} \times 10 \cr & = {\text{Rs}}{\text{.}}\,\frac{{20}}{9} \cr} $$
so Loss = $$\left( {\frac{9}{4} - \frac{{20}}{9}} \right) = \frac{1}{{36}}$$
Now, if loss is Rs.$$\frac{1}{{36}}$$, number of article = 10
So If loss is Rs. 3, number of article = 36 × 10 × 3 = 1080

Let the total C.P. of all the articles be Rs. x.
Then,
C.P. of 80% of the articles = 80% of Rs. x.
$$ = {\text{Rs}}.\frac{{4x}}{5}$$
C.P. of the remaining articles
$$\eqalign{ & = {\text{Rs}}.\left( {x - \frac{{4x}}{5}} \right) \cr & = {\text{Rs}}.\frac{x}{5} \cr & {\text{Total S}}{\text{.P}}{\text{.}} \cr & = Rs.\left( {110\% {\text{ of }}\frac{{4x}}{5} + 60\% {\text{ of }}\frac{x}{5}} \right) \cr & = {\text{Rs}}.\left( {\frac{{22x}}{{25}} + \frac{{3x}}{{25}}} \right) \cr & = {\text{Rs}}{\text{. }}x. \cr} $$
Since C.P. = S.P. there is no profit no loss

Total C.P. = Rs. (120 × 3) = Rs. 360
Total S.P. = Rs. (40 × 4 + 60 × 5 + 20 × 3) = Rs. 520
Profit = Rs. (520 - 360) = Rs. 160
$$\eqalign{ & \therefore {\text{Profit}}\% \cr & = \left( {\frac{{160}}{{360}} \times 100} \right)\% \cr & = \left( {\frac{{400}}{9}} \right)\% \cr & = 44\frac{4}{9}\% \cr} $$

Let the number of toffees bought be (2 x 5) = 10
C.P. of 10 toffees $$ = {\text{Rs}}{\text{.}}\,\left( {\frac{1}{2} \times 10} \right) = {\text{Rs}}{\text{.}}\,5$$
S.P. of 10 toffees $$ = {\text{Rs}}{\text{.}}\,\left( {\frac{1}{5} \times 10} \right) = {\text{Rs}}{\text{.}}\,2$$
$$\eqalign{ & {\text{Loss}}\% = \left( {\frac{3}{5} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 60\% \cr} $$