Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

Let Selling price of 1 meters cloth = Rs. 1
Selling price of 33 meters cloth = Rs. 33
Cost price of 1 meter cloth = Rs. x
Cost price of 33 meters cloth = Rs. 33x
According to the question,
Profit = Selling price - Cost price
$$\eqalign{ & \Rightarrow 11x = 33 - 33x \cr & \Rightarrow 44x = 33 \cr & \Rightarrow x = \frac{{33}}{{44}} = \frac{3}{4} \cr & {\text{Cost price of 1 metre}} \cr & = {\text{Rs}}{\text{.}}\frac{3}{4} \cr & {\text{Cost price of 33 metres}} \cr & = \frac{3}{4} \times 33 \cr & = {\text{Rs}}.\frac{{99}}{4} \cr} $$
Selling price of 33 meters = Rs. 33
Profit = Selling price = Cost price
$$\eqalign{ & = 33 - \frac{{99}}{4} \cr & = \frac{{33}}{4} \cr & \therefore {\text{Profit }}\% \cr & {\text{ = }}\frac{{\frac{{33}}{4}}}{{\frac{{99}}{4}}} \times 100 \cr & = \frac{{33}}{{99}} \times 100 \cr & = \frac{1}{3} \times 100 \cr & = 33\frac{1}{3}\% \cr} $$

Alternate :
Let Selling price of 1 meters cloth = Rs. 1
Selling price of 33 meters cloth = Rs. 33
33 Selling price - 33 Cost price = 11 Cost price
33 Selling price = 44 Cost price
$$\eqalign{ & \frac{{{\text{Selling price}}}}{{{\text{Cost price}}}} = \left. {\frac{4}{3}} \right\rangle 1 \cr & {\text{Profit = 1}} \cr & {\text{Profit }}\% = \frac{1}{3} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 33\frac{1}{3}\% \cr} $$

Let the selling price of 1 meter cloth = Rs. 1
The Selling price of 33 meters cloth
= 1 × 33 = Rs. 33
Cost of 1 meter cloth = Rs. x
Cost price 33 meters cloth = x × 33 = Rs. 33x
According to the question,
Profit = Selling price - Cost price
$$\eqalign{ & \Rightarrow 11 = 33 - 33x \cr & \Rightarrow 33x = 22 \cr & \Rightarrow x = \frac{{22}}{{33}} = \frac{2}{3} \cr} $$
Cost price of 1 meter cloth $$ = {\text{Rs}}{\text{.}}\frac{2}{3}$$
Cost price of 33 meters cloth
$$\eqalign{ & = \frac{2}{3} \times 33 \cr & = {\text{Rs}}.22 \cr} $$
Selling price of 33 meters cloth = Rs. 33
Profit = Selling price - Cost price
= 33 - 22 = 11
$$\eqalign{ & {\text{Profit}}\% \cr & = \frac{{11}}{{22}} \times 100 \cr & = 50\% \cr} $$

According to the question,
Cost price = Rs. 840
10% Profit on cost price
$$\eqalign{ & = \frac{{10}}{{100}} \times 840 \cr & = {\text{Rs}}{\text{. }}84 \cr & \therefore {\text{Selling price}} \cr & = 840 + 84 \cr & = {\text{Rs}}{\text{. 924}} \cr} $$
New buyer cost price
$$ = {\text{Rs}}{\text{. 924}}$$
5% loss on Cost price
$$\eqalign{ & = \frac{5}{{100}} \times 924 \cr & = {\text{Rs}}{\text{. }}46.2 \cr & {\text{Selling price}} \cr & = {\text{Rs}}{\text{. 924}} - 46.2 \cr & = {\text{Rs}}{\text{. }}877.80 \cr} $$

Let the total initial cost of production be Rs. 100
Then,
manufacturing cost = Rs. 60
Cost of raw materials = Rs. 40
Original Selling Price
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {100 + \frac{{60}}{4}} \right) \cr & = {\text{Rs}}{\text{. }}115 \cr} $$
New cost of raw materials = 130% of Rs. 40 = Rs. 52
New Manufacturing cost = 120% of Rs. 60 = Rs. 72
New cost of the product = Rs. (52 + 72) = Rs. 124
New S.P. = 160% of Rs. 115
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{160}}{{100}} \times 115} \right) \cr & = {\text{Rs}}{\text{. }}184 \cr} $$
New profit = Rs. (184 - 124) = Rs. 60
$$\eqalign{ & \therefore {\text{New profit }}\% \cr & = \left( {\frac{{60}}{{124}} \times 100} \right)\% \cr & = 48.39\% \cr} $$

Original C.P. of the product = Rs. 8.
Original manufacturing cost
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{3}{4} \times 8} \right) \cr & = {\text{Rs}}{\text{. }}6 \cr} $$
Original cost of raw material
$$\eqalign{ & = {\text{Rs}}.\left( {8 - 6} \right) \cr & = {\text{Rs}}{\text{. }}2 \cr} $$
New manufacturing cost
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{5}{3} \times 6} \right) \cr & = {\text{Rs}}{\text{. }}10 \cr} $$
New cost of raw material
$$\eqalign{ & = {\text{Rs}}.\left( {\frac{{12}}{5} \times 2} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{24}}{5} \cr} $$
New S.P. of the product
$$\eqalign{ & = {\text{Rs}}.\left( {10 + \frac{{24}}{5}} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{74}}{5} \cr} $$
$$\eqalign{ & \therefore {\text{Desired S}}{\text{.P}}{\text{.}} \cr & = 125\% {\text{ of Rs}}.\frac{{74}}{5} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{125}}{{100}} \times \frac{{74}}{5}} \right) \cr & = {\text{Rs}}.18.50 \cr} $$

In this type of question go through option
Option : C
Cost price = Rs. 50
Gains as much percentage as the cost price of the article means 50% gains
50% of cost price
50% of Rs. 50 = Rs. 25
Selling price = Cost price + Profit
Selling price = 50 + 25
Selling price = Rs. 75

According to the question,
Selling price = Rs. 144
Cost price is equal to percentage of profit.
Note : In this type of question go through option.
Option = B
Cost price = Rs. 80
Profit % = 80%
Selling price
$$\eqalign{ & = 80 + \frac{{80}}{{100}} \times 80 \cr & = {\text{Rs}}{\text{.144 (Satisfied)}} \cr} $$

Let n erasers be available for a rupee
Reduced Price $$ = \frac{{75}}{{100}} \times 1 = \,\frac{3}{4}$$
$$\frac{3}{4}$$ rupee fetch n erasers = 1 Rupee will fetch $$\left( {{\text{n}} \times \frac{4}{3}} \right)$$  erasers
Therefore,
$$\eqalign{ & \frac{{4n}}{3} = n + 2 \cr & \Rightarrow 4n = 3n + 6 \cr & \Rightarrow n = 6 \cr} $$
Now total number of erasers are available for a rupee = 6 + 2 =8

M.P. = Rs. 272000
Discount = Rs. [(4% of 200000) + (2.5% of 72000)]
= Rs. (8000 + 1800)
= Rs. 9800
Actual price
= Rs. (272000 - 9800)
= Rs. 2,62,200

$$\eqalign{ & {\text{Rate of discount}} \cr & = \left( {\frac{{12}}{{80}} \times 100} \right)\% \cr & = 15\% \cr} $$