Profit and Loss - 02

Explanation:-

Cost price of 28 articles = Selling price of 21 articles $$\frac{{{\text{CP}}}}{{{\text{SP}}}} = \frac{{21}}{{28}} = \frac{3}{4}$$ Profit = Selling price - Cost price = 4 - 3 = 1 $$\eqalign{ & {\text{Profit }}\% = \frac{1}{3} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 33\frac{1}{3}\% \cr}$$

Explanation:-

Selling price after given 20% discount $$\eqalign{ & = 150 \times \frac{{\left( {100 - 20} \right)}}{{100}} \cr & = 120 \cr & {\text{So,}} \cr & \Rightarrow 120 \times \frac{x}{{100}} = 108 \cr & \Rightarrow x = 90 \cr}$$ ∴ Required additional discount = (100 - 90)% = 10%

Explanation:-

6 selling price = 8 cost price $$\eqalign{ & \frac{{{\text{SP}}}}{{{\text{CP}}}} = \left. {\frac{4}{3}} \right)1 \to {\text{Profit}} \cr & {\text{Profit}} = {\text{1}} \cr & {\text{Profit }}\% = \frac{1}{3} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 33\frac{1}{3}\% \cr}$$

Explanation:-

Let cost price be Rs. 100
The selling price be Rs. x
Then, $$\eqalign{ & \frac{{95}}{{100}}x = 123.50 \cr & \Rightarrow x = {\text{Rs}}{\text{.}}\left( {\frac{{12350}}{{95}}} \right) \cr & \Rightarrow x = {\text{Rs}}{\text{.130}} \cr}$$ Now, selling price = Rs. 130
Cost price = Rs. 100
∴ Profit % = 30%

Explanation:-

Let the marked price of the shirt and trousers be Rs. x and Rs. 2x respectively.
Let the discount offered on trousers be y%
Then, Selling price of shirt $$\eqalign{ & = 60\% {\text{ of Rs}}{\text{. }}x \cr & = {\text{Rs}}\left( {\frac{{60}}{{100}} \times x} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{3x}}{5} \cr & {\text{Selling price of trousers}} \cr & = \left( {100 - y} \right)\% {\text{ of Rs}}{\text{. }}2x \cr & = {\text{Rs}}.\left[ {\frac{{\left( {100 - y} \right)}}{{100}} \times 2x} \right] \cr & = {\text{Rs}}.\left[ {\frac{{\left( {100 - y} \right)x}}{{100}}} \right] \cr}$$ Combined Selling price of shirt and trousers $$\eqalign{ & = 70\% {\text{ of Rs}}{\text{.}}\left( {x + 2x} \right) \cr & = {\text{Rs}}.\left( {\frac{{70}}{{100}} \times 3x} \right) \cr & = {\text{Rs}}.\frac{{21x}}{{10}} \cr & \therefore \frac{{3x}}{5} + \frac{{\left( {10 - y} \right)x}}{{50}} = \frac{{21x}}{{10}} \cr & \Rightarrow \frac{{130 - y}}{{50}} = \frac{{21}}{{10}} \cr & \Rightarrow 1300 - 10y = 150 \cr & \Rightarrow y = 25 \cr}$$

Explanation:-

$$15\% = \frac{3}{{20}},$$

Cost Price		Selling Price
$$\mathop { \downarrow \times 18.75}\limits_{375\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}^{20\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}$$		$$\mathop { \downarrow \times 18.75}\limits_{318.75\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}^{17\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}$$

Explanation:-

Cost Price	:	Markde Price
(100 - Discount%)	:	(100 + Profit%)
100 - 5%	:	100 + 33%
$$\underbrace {95\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,133}_{38}$$

$$\eqalign{ & {\text{Required }}\% = \frac{{38}}{{95}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 40\% \cr}$$

Explanation:-

Selling price of 1 article = Rs. 45
Let marked price of each article be Rs. x
Then, $$\eqalign{ & \frac{{90}}{{100}}x = 45 \cr & x = {\text{Rs}}{\text{.}}\left( {\frac{{45 \times 100}}{{90}}} \right) \cr & \,\,\,\,\,\, = {\text{Rs}}{\text{. 50}} \cr & {\text{CP}} = {\text{Rs}}{\text{.}}\left( {\frac{{100}}{{150}} \times 45} \right) \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 30}} \cr}$$ When no discount is given,
Cost price = Rs. 30,
Selling price = Rs. 50
∴ Required profit % $$\eqalign{ & = \left( {\frac{{20}}{{30}} \times 100} \right)\% \cr & = 66\frac{2}{3}\% . \cr}$$

Explanation:-

Selling Price = Rs. 25935
Let marked price be Rs. x
Then, $$\eqalign{ & = {\text{91}}\% {\text{ of }}x{\text{ = 25935}} \cr & x{\text{ = }}\left( {\frac{{25935 \times 100}}{{91}}} \right) \cr & \,\,\,\,\,\, = 28500. \cr & {\text{Cost Price}} \cr & = {\text{Rs}}.\left( {\frac{{100}}{{103.74}} \times 25935} \right) \cr & = {\text{Rs}}{\text{. 25000}}{\text{.}} \cr}$$ Now Cost price = Rs. 25000
S.P. = Rs. 28500
Profit = Rs. (28500 - 25000) = Rs. 3500 $$\eqalign{ & \therefore {\text{ Required profit }}\% \cr & = \left( {\frac{{3500}}{{25000}} \times 100} \right)\% \cr & = 14\% . \cr}$$

Explanation:-

$$\eqalign{ & {\text{Marked Price}} = {\text{Rs}}{\text{.30}}{\text{.}} \cr & {\text{Selling Price}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {\frac{{85}}{{100}} \times 30} \right) - 1.50} \right] \cr & = {\text{Rs}}{\text{.}}\left( {25.50 - 1.50} \right) \cr & = {\text{Rs}}{\text{.2}}4. \cr & {\text{Let }}C.P.be{\text{Rs}}{\text{. }}x. \cr & {\text{Then,}} \cr & {\text{120}}\% {\text{ of }}x = {\text{24}} \cr & \Rightarrow x = \left( {\frac{{24 \times 100}}{{120}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}20. \cr}$$