Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

According to the question,
Cost price of 73 articles are
= Rs. 5110
Cost price of 1 articles are
$$\eqalign{ & = \frac{{5110}}{{73}} \cr & = {\text{Rs}}{\text{. 70}} \cr} $$
Selling price of 89 articles are = Rs. 5607
Selling price of 1 articles is
$$\eqalign{ & = \frac{{5607}}{{89}} \cr & {\text{ = Rs}}{\text{. 63}} \cr} $$
Loss = Cost price - Selling price
Loss = 70 - 63 = Rs. 7
$$\eqalign{ & {\text{Loss}}\% = \frac{7}{{70}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$

CP of 1 orange $$ = {\text{Rs}}{\text{.}}\,\frac{{34}}{8} = {\text{Rs}}{\text{.}}\,4.25$$
SP of 1 orange $$ = {\text{Rs}}{\text{.}}\,\frac{{57}}{{12}} = {\text{Rs}}{\text{.}}\,4.75$$
Profit on each apple = (4.75 - 4.25) = Rs. 0.50
∴ Number of apples required $$ = \frac{{45}}{{0.50}} = 90$$

Let the quantity sold at 18% profit be $$x$$ kg and let C.P. per kg be Rs. 1
Then,
quantity sold at 8% profit = (1000 - $$x$$) kg.
Total C.P. = Rs. 1000
Total S.P. = Rs. [108% of (1000 - x) + 118% of $$x$$]
  $$ = {\text{Rs}}.\left[ {\frac{{27}}{{25}}\left( {1000 - x} \right) + \frac{{59x}}{{50}}} \right]$$      $$ = {\text{Rs}}.\left( {1080 + \frac{x}{{10}}} \right)$$
$$\eqalign{ & \therefore 1080 + \frac{x}{{10}} = 114\% {\text{ of }}1000 \cr & \Rightarrow 1080 + \frac{x}{{10}} = 1140. \cr & \Rightarrow \frac{x}{{10}} = 60 \cr & \Rightarrow x = 600 \cr} $$

Let the total value be Rs. x
$$\eqalign{ & {\text{value of }}\frac{2}{3}{\text{rd}} = {\text{Rs}}{\text{.}}\frac{{2x}}{3} \cr & {\text{value of}}\frac{1}{3}{\text{rd}} = {\text{Rs}}.\frac{x}{3} \cr & {\text{Total S}}{\text{.P}}{\text{.}} \cr & = {\text{Rs}}.\left[ {\left( {106\% {\text{ of }}\frac{{2x}}{3}} \right) + \left( {97\% {\text{ of }}\frac{x}{3}} \right)} \right] \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{53x}}{{75}} + \frac{{97x}}{{300}}} \right) \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{309x}}{{300}}} \right) \cr & \therefore \frac{{309x}}{{300}} - x = 540 \cr & \Rightarrow \frac{{9x}}{{300}} = 540 \cr & \Rightarrow x = \left( {\frac{{540 \times 300}}{9}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 18000 \cr} $$

Let article purchased be 1
1 articale = Rs. 10
1 articale = Rs. 14
CP of 2 article = 10 + 14 = Rs. 24
CP of 1 article = $$\frac{{24}}{2}$$ = Rs. 12
SP of 1 article = Rs. 13
Profit = 13 - 12 = Rs. 1
$$\eqalign{ & {\text{Profit}}\% = \frac{1}{{12}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{25}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 8\frac{1}{3}\% \cr} $$

Man purchased 15 oranges of each type
CP of 1^st type $$ = \frac{{40}}{3} \times 15 = 200$$
CP of 2^nd type $$ = \frac{{60}}{5} \times 15 = 180$$
Total cost price = (200 + 180) = 380
Total selling price $$ = \frac{{50}}{3} \times 30 = 500$$
∴ Profit percentage
$$\eqalign{ & = \frac{{500 - 380}}{{380}} \times 100 \cr & = \frac{120}{380}\times100 \cr & = \frac{600}{19}\% \cr & = 31.57\% \cr & \approx 32\% \cr} $$

According to the question
Cost Price
= 30 × 9.50 + 30 × 8.50
= 30[9.50 + 8.50]
= 30 × 18
= Rs. 540
Selling Price
= 60 × 8.90
= Rs. 534
Loss = Cost price - Selling price
= 540 - 534
= Rs. 6

Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y.
Then,
= 4x + 9y = 13400 ......(i)
and,
10% of 4x + 20% of 9y = 1880
$$\eqalign{ & \Rightarrow \frac{2}{5}x + \frac{9}{5}y = 1880 \cr & \Rightarrow 2x + 9y = 9400....({\text{ii}}) \cr} $$
Solving (i) and (ii), we get:
x = 2000 and y = 600
∴ Cost price of each horse = Rs. 2000

Let C.P. of clock A be Rs. x and that of clock B be Rs. (650 - x).
Then,
120% of x = 75% of (650 - x)
$$\eqalign{ & \Rightarrow 650 - x = \frac{{120}}{{75}}x \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{8}{5}x \cr & \Rightarrow \frac{{13}}{5}x = 650 \cr & \Rightarrow x = \left( {\frac{{650 \times 5}}{{13}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 250 \cr & \therefore {\text{C}}{\text{.P}}{\text{. of A}} = {\text{Rs}}{\text{. }}250 \cr & {\text{C}}{\text{.P}}{\text{. of B}} = {\text{Rs}}{\text{. }}400 \cr} $$

Let 5 kg of cheaper be mixed with 3 kg of dearer.
Then,
Total CP = Rs. (180 x 5 + 200 x 3) = Rs. 1500
Total SP = Rs. (210 x 8) = Rs. 1680
$$\eqalign{ & {\text{Gain}}\% = \left( {\frac{{180}}{{1500}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr} $$