Profit and Loss - 04

Explanation:-

$$20\% = \frac{{1 \to {\text{Profit}}}}{{5 \to {\text{CP}}}}$$ Selling price = 6 units → 390 $$\eqalign{ & {\text{5 units }} \to \frac{{390 \times 5}}{6} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 325 \cr}$$

Explanation:-

$$\eqalign{ & {\text{Loss}} = {\text{Rs}}.\left[ {\left( {92\% {\text{ of }}92\% {\text{ of }}900} \right)} \right] \cr & = {\text{Rs}}.\left[ {\left( {\frac{{92}}{{100}} \times \frac{{92}}{{100}} \times 900} \right) - \left( {\frac{{84}}{{100}} \times 900} \right)} \right] \cr & = {\text{Rs}}.\left( {761.76 - 756} \right) = {\text{Rs}}.5.76 \cr & = {\text{Loss of Rs}}{\text{. }}5.76 \cr}$$

Explanation:-

Let the M.P. be Rs. x
Then,
(90% of 80% of x) - (70% of x) = 72 $$\eqalign{ & \Rightarrow \left( {\frac{{90}}{{100}} \times \frac{{80}}{{100}} \times x} \right) - \left( {\frac{{70}}{{100}} \times x} \right) = 72 \cr & \Rightarrow \frac{{72}}{{100}}x - \frac{{70}}{{100}}x = 72 \cr & \Rightarrow \frac{2}{{100}}x = 72 \cr & \Rightarrow x = \left( {\frac{{72 \times 100}}{2}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 3600. \cr}$$

Explanation:-

Selling price of 1 potatoes $$\eqalign{ & = {\text{Rs}}{\text{.}}\frac{{63}}{{12}} \cr & = {\text{Rs}}{\text{.}}\frac{{21}}{4} \cr & {\text{CP}} \times \frac{{\left( {100 + {\text{P}}} \right)}}{{100}} = {\text{SP}} \cr & {\text{CP}} \times \frac{{105}}{{100}} = \frac{{21}}{4}{\text{ }} \cr & {\text{CP}} = {\text{Rs}}{\text{. 5}} \cr}$$ Gain or loss percent by selling 50 kg of the same potatoes for Rs. 247.50
Cost price of 50 kg potatoes
= 50 × 5
= Rs. 250
Loss = 250 - 247.50 = Rs. 2.50 $$\eqalign{ & {\text{Loss }}\% = \frac{{2.50}}{{250}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\% \cr}$$

Explanation:-

Selling price of 4 article = Rs. 1
Loss = 4%
Cost price of 4 articles $${\text{ = 1}} \times \frac{{100}}{{96}} = \frac{{100}}{{96}}$$ Cost price of 3 articles $${\text{ = }}\frac{{100}}{{96}} \times \frac{3}{4} = \frac{{75}}{{96}}$$ New selling price of 3 articles = Rs. 1 $$\eqalign{ & {\text{Profit }}\% \cr & = \frac{{\frac{{1 - 75}}{{96}}}}{{\frac{{75}}{{96}}}} \times 100 \cr & = \frac{{21}}{{75}} \times 100 \cr & = 28\% \cr}$$

Explanation:-

Let the original price be Rs. x.
Then,
95% of 88% of x = 209 $$\eqalign{ & \Rightarrow x = \left( {\frac{{209 \times 100 \times 100}}{{95 \times 88}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 250. \cr & = {\text{Rs}}{\text{. }}250. \cr}$$

Explanation:-

According to the question,
Cost price = Rs. 25
Selling price = Rs. 30
Profit = Selling price - Cost price
= 30 - 25
= Rs. 5 $$\eqalign{ & {\text{Profit}}\% = \frac{5}{{25}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 20\% \cr}$$

Explanation:-

Profit of A = Profit of B (given)
10% A = 15% B $$\eqalign{ & \frac{{\text{A}}}{{\text{B}}} = \frac{{15}}{{10}} = \frac{3}{2} \cr & {\text{A}}:{\text{B}} = 3:2 \cr}$$ Now with the help of option,
check the ratio of cost price of A and B
Option : C
3000 : 2000
3 : 2

Explanation:-

S.P. = 95% of 95% of Rs. 80 $$\eqalign{ & = {\text{Rs}}.\left( {\frac{{95}}{{100}} \times \frac{{95}}{{100}} \times 80} \right) \cr & = {\text{Rs}}.72.20. \cr}$$

Explanation:-

According to the question, $$\eqalign{ & {\text{C}}{\text{.P}}{\text{. = }}\frac{{90}}{{100}}{\text{S}}{\text{.P}}{\text{.}} \cr & \frac{{{\text{C}}{\text{.P}}{\text{.}}}}{{{\text{S}}{\text{.P}}{\text{.}}}}{\text{ = }}\left. {\frac{9}{{10}}} \right\rangle {\text{1 unit profit}} \cr & {\text{Profit }}\% = \frac{1}{9} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\frac{1}{9}\% {\text{ }} \cr}$$