Profit And Loss - Aptitude MCQ Questions and Solutions with Explanations

Seller uses faulty weight instead of 2 kg i.e., 2000 gram
Gain = 25%
Let's say error = $$a$$
$$\eqalign{ & {\text{Profit }}\% = \frac{{{\text{Error}}}}{{{\text{True weight}} - {\text{Error}}}} \times 100 \cr & 25 = \frac{a}{{2000 - a}} \times 100 \cr & \frac{1}{4} = \frac{a}{{2000 - a}} \cr & 2000 - a = 4a \cr & 2000 = 5a \cr & {\text{So, }}a = 400{\text{ gm}}{\text{.}} \cr} $$

\[\begin{array}{*{20}{c}} {}&{\text{I}}&{{\text{II}}} \\ {{\text{Cost Price}} \to }&{{{50}_{ \times 57}}}&{{{50}_{43}}} \\ {{\text{Profit/Loss}} \to }&{ - 7}&{ + 7} \\ {{\text{Sale Price}} \to }&{{{43}_{ \times 51}}}&{{{57}_{ \times 43}}} \end{array}\]
Cost price = 50(57 + 43)
= 5000 unit → 624
= 1 unit → $$\frac{{624}}{{5000}}$$
Difference of Cost price $$ = \frac{{\left( {50 \times 14} \right) \times 624}}{{5000}} = 87.36$$

Cost of one pencil = Rs. $$\frac{5}{4}$$
Cost of 60 pencil = $$\frac{5}{4}$$ × 60 = Rs. 75
Cost of single second-type pencil = Rs. $$\frac{3}{2}$$
Cost of 60 second-type pencil = $$\frac{3}{2}$$ × 60 = Rs. 90
Total cost price = 75 + 90 = Rs. 165
Selling price of one pencil = Rs. $$\frac{4}{3}$$
Total selling price = $$\frac{4}{3}$$ × 120 = Rs. 160
Total loss = 165 - 160 = Rs. 5
Loss % = $$ = \frac{5}{{165}} \times 100 = 3\frac{1}{{33}}\% $$
∴ The loss incurred is $$3\frac{1}{{33}}\% $$

Selling price of tea = Rs. 9 per cup
Profit % = 50%
∴ Cost price of tea = 9 × $$\frac{{100}}{{150}}$$ = Rs. 6 per cup
New cost price of tea after 25% increased,
New cost price = 6 × $$\frac{{125}}{{100}}$$ = Rs. 7.50
New selling price = Rs. 10
∴ Profit = (10 - 7.5) = Rs 2.50
∴ Profit % $$ = \frac{{2.50}}{{7.50}} \times 100 = 33\frac{1}{3}\% $$

Let's assume that the cost price of the goods for the man is Rs. 100.
Given:
Profit = 20% of the selling price
Cost Price = Rs. 100
Profit = 20% of Selling Price
Profit = 0.2 × Selling Price
Selling Price = Cost Price + Profit
Selling Price = Rs. 100 + 0.2 × Selling Price
0.8 × Selling Price = Rs. 100
Selling Price = $$\frac{{{\text{Rs}}{\text{. }}100}}{{0.8}}$$
Selling Price = Rs. 125
So, the man sells the goods at Rs. 125.
Now, after the price at which he buys the goods increases by 10%, the new cost price will be:
New Cost Price = Rs. 100 + 10% of Rs. 100
New Cost Price = Rs. 100 + Rs. 10
New Cost Price = Rs. 110
He sells the goods at an 8% higher price, so the new selling price will be:
New Selling Price = Rs. 125 + 8% of Rs. 125
New Selling Price = Rs. 125 + Rs. 10
New Selling Price = Rs. 135
New Profit = New Selling Price - New Cost Price
New Profit = Rs. 135 - Rs. 110
New Profit = Rs. 25
Now, let's calculate the profit percentage based on the new selling price and the new cost price:
Profit Percentage = $$\frac{{{\text{Profit}}}}{{{\text{Cost Price}}}} \times 100$$
Profit Percentage = $$\frac{{25}}{{100}} \times 100$$
Profit Percentage ≈ 22.7%
Therefore, the man's profit percentage, correct to one decimal place, is approximately 22.7%.

A person sold 25 article Rs. 2500
Selling price of 1 article $$ = \frac{{2500}}{{25}} = 100$$
Cost price of 1 article $$ = 100 \times \frac{{100}}{{90}} = \frac{{1000}}{9}$$
New selling price of 1 article = $$ = \frac{{1000}}{9} \times \frac{{120}}{{100}} = \frac{{400}}{3}$$
Number of articles sold in Rs. 2400 $$ = 2400 \div \frac{{400}}{3} = 18$$

Let the length of scale be 'x' metres
Let the cost price per metre of cloth be Rs. 100
Cost price of cloth with false scale Rs. 93 per metre and gains 24% profit
Cost price of x metre length cloth = 100x
According to the question,
⇒ 100x + 24% of 100x = 93
⇒ 100x + 24x = 93
⇒ 124x = 93
⇒ x = $$\frac{{93}}{{124}}$$
⇒ x = 0.75 metre
∴ The actual length he uses instead of 1 metre is 75 cm.

$$\eqalign{ & {\text{Let salary}} = 100 \cr & {\text{Then, }}100 \times \frac{{50}}{{100}} \times \frac{{150}}{{100}} \times \frac{{200}}{{100}} = 150\% \cr & {\text{Gain}} = 150 - 100 = \boxed{50\% } \cr} $$

\[\begin{array}{*{20}{c}} {}&{\text{I}}&{{\text{II}}} \\ {{\text{Cost Price}} \to }&{{{20}_{ \times 19}}}&{{{20}_{ \times 21}}} \\ {{\text{Profit/Loss}} \to }&{ + {1_{ \times 19}}}&{ - {1_{ \times 21}}} \\ {{\text{Sales Price}} \to }&{{{21}_{ \times 19}}}&{{{19}_{ \times 21}}} \end{array}\]
21 × 19 unit → 9975
1 unit → 25
Loss = 2 unit = 2 × 25 = Rs. 50

$$\eqalign{ & {\text{Profit }}\% = 12 + 12 + \frac{{12 \times 12}}{{100}} \cr & = 24 + 1.44 \cr & = 25.44\% \cr} $$