Profit and Loss - 01

Explanation:-

$$\eqalign{ & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{.340}}{\text{.}} \cr & {\text{Let marked price be Rs}}{\text{. }}x{\text{.}} \cr & {\text{Then,}} \cr & {\text{ = 85}}\% {\text{ of }}x = {\text{340}} \cr & \Rightarrow x{\text{ = }}\left( {\frac{{340 \times 100}}{{85}}} \right) = 400. \cr & {\text{Cost Price}} \cr & = {\text{Rs}}{\text{.}}\left( {100 \times \frac{3}{{340}} \times 340} \right) \cr & = {\text{Rs}}{\text{. 300}}{\text{.}} \cr & {\text{Now, C}}{\text{.P}}{\text{. = Rs}}{\text{. 300}}{\text{.}} \cr & {\text{S}}{\text{.P}}{\text{.}} = {\text{Rs}}{\text{. 400}}{\text{.}} \cr & \therefore {\text{ Required profit }}\% \cr & = \left( {\frac{{100}}{{300}} \times 100} \right)\% \cr & = 33\frac{1}{3}\% . \cr}$$

Explanation:-

Selling price of washing machine = Rs. 8500
Loss % = 15%
Cost price of washing machine $$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{100}}{{85}} \times 8500} \right) \cr & = {\text{Rs}}{\text{.10000}} \cr}$$

Explanation:-

Price of the saree including sales tax = Rs. 5225
Cost price without sales tax $$\eqalign{ & = \frac{{5225}}{{112}} \times 100 \cr & = 4665 \cr & {\text{The price decreased}} \cr & = {\text{Rs}}{\text{.}}\left( {5225 - 4665} \right) \cr & = {\text{Rs}}{\text{. }}560 \cr}$$

Explanation:-

Let the cost price of article be Rs. x
Profit = 12%
Rate of sales tax = 10%
Sale price of an article including sales tax = Rs. 1232
According to the question, $$\eqalign{ & \Rightarrow \frac{{112x}}{{100}} + \frac{{112x \times 10}}{{10000}} = 1232 \cr & \Rightarrow \frac{{1120x + 112x}}{{1000}} = 1232 \cr & \Rightarrow 1232x = 1232 \times 1000 \cr & \Rightarrow x = {\text{Rs}}{\text{. }}1000 \cr}$$

Explanation:-

$$\eqalign{ & \% {\text{ Loss }} = 20\% \cr & 20\% = \frac{1}{5} \cr}$$ It Cost price = 5 units
Loss = 1 units
Selling price = 5 - 1 = 4 units
Selling price = 4
we make it equal to Cost price that is (5)
So, we multiply Selling price by $$\eqalign{ & = \frac{5}{4} \cr & {\text{Selling price}} = 4 \times \frac{5}{4} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5{\text{ }} \cr}$$

Explanation:-

Let the marked price be of book be Rs. 100
Cost price of the retailer = Rs. (100 - 30) = Rs. 70
Selling price for the retailer = Rs. 90
∴ Profit percent $$\eqalign{ & = \left( {\frac{{90 - 70}}{{70}}} \right) \times 100 \cr & = \left( {\frac{{20}}{{70}}} \right) \times 100 \cr & = \frac{{200}}{7} \cr & = 28\frac{4}{7}\% \cr}$$

Explanation:-

$$\eqalign{ & {\text{Marked price of shirt}} \cr & = {\text{Rs}}{\text{.1080}} \cr & {\text{Selling price of shirt}} \cr & = {\text{Rs}}{\text{.1080}} - \frac{{1080 \times 12}}{{100}} \cr & = {\text{Rs}}{\text{.}}\left( {1080 - 129.60} \right) \cr & = {\text{Rs}}.950.40 \cr & {\text{Let CP of shirt is Rs}}{\text{. }}x \cr & \therefore x + \frac{{x \times 8}}{{100}} = 950.40 \cr & \Rightarrow \frac{{108x}}{{100}} = 950.40 \cr & \Rightarrow x = 950.40 \times \frac{{100}}{{108}} \cr & \Rightarrow x = {\text{Rs}}{\text{. }}880 \cr}$$

Explanation:-

Let the cost price of a article be x
Then, loss = (6800 - x)
Again, profit = (7850 - x)
According to given information we get
Now, $$\eqalign{ & \left( {7850 - x} \right) = \frac{{\left( {6800 - x} \right)}}{2} \cr & \Rightarrow 17500 - 2x = 6800 - x \cr & \Rightarrow x = 15700 - 6800 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 8900 \cr & {\text{If profit }}\% = 20\% {\text{ then}} \cr & \therefore {\text{SP}} = \frac{{8900 \times 120}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.10680}} \cr}$$

Explanation:-

$$\eqalign{ & {\text{Total selling price}} \cr & = \frac{{750 \times 100}}{{100}} + \frac{{750 \times 96}}{{100}} \cr & = 795 + 720 \cr & = 1515 \cr & {\text{Profit}} = 1515 - 1500 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 5}} \cr & \therefore {\text{Profit }}\% = \frac{{15}}{{1500}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\% {\text{ gain}} \cr}$$

Explanation:-

VAT % = 13.5%
Cost price (including VAT) = Rs. 6810 $$\eqalign{ & \therefore {\text{List price}} = \frac{{6810}}{{113.5}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}6000 \cr}$$