Profit and Loss - 03

Explanation:-

Let Cost price = Rs. 100
Then,
Selling price = Rs. 120
Let marked price be Rs. x
Then,
90% of x = 120 $$\eqalign{ & \Rightarrow x{\text{ = }}\left( {\frac{{120 \times 100}}{{90}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 133\frac{1}{3}. \cr & \therefore {\text{Marked price}} \cr & = {\text{33}}\frac{1}{3}\% {\text{ above C}}{\text{.P}}{\text{.}} \cr}$$

Explanation:-

$$\eqalign{ & {\text{Let selling price}} = {\text{100}} \cr & \underbrace {\mathop {{\text{Loss}}}\limits_{80} \,\,\,\,\,\,\,\,\mathop {{\text{Profit}}}\limits_{115} }_{{\text{Selling price }}35} \cr & {\text{35}} \to {\text{70}} \cr & {\text{1}} \to \frac{{70}}{{35}} = 2{\text{ }} \cr & \therefore {\text{Cost price}} = 100 \times 2 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}200 \cr}$$

Explanation:-

$$\eqalign{ & {\text{Total discount by A}} \cr & = 20000 \times \frac{8}{{100}} + 16000 \times \frac{5}{{100}} \cr & = 1600 + 800 \cr & = {\text{Rs}}{\text{. 2400}} \cr & {\text{Selling price of A}} \cr & = 36000 - 2400 \cr & = {\text{Rs}}.33600 \cr & {\text{Selling price of B}} \cr & = 36000 \times \frac{{100 - 7}}{{100}} \cr & = 36000 \times \frac{{93}}{{100}} \cr & = {\text{Rs}}{\text{. 33480}} \cr}$$

Explanation:-

Marked price = Rs. 130
Final price = 90% of 90% $$\eqalign{ & {\text{ = Rs}}{\text{.}}\left( {\frac{{90}}{{100}} \times \frac{{90}}{{100}} \times 130} \right) \cr & = {\text{Rs}}{\text{.105}}{\text{.30}}{\text{.}} \cr}$$ ∴ Increase in price = (105.30 - 100)% = 5.3 years.

Explanation:-

$$\eqalign{ & {\text{S}}{\text{.P}}{\text{. = Rs}}{\text{. }}x \cr & {\text{Profit = 10}}\% \cr & {\text{C}}{\text{.P}}{\text{. = Rs}}{\text{.}}\left( {\frac{{100}}{{110}} \times x} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{ Rs}}{\text{.}}\frac{{10x}}{{11}}. \cr & {\text{M}}{\text{.P}}{\text{. = Rs}}{\text{. }}2x, \cr & {\text{Discount = 20}}\% {\text{.}} \cr}$$ S.P. at trade fair = 80% of Rs. 2x $$\eqalign{ & {\text{ = Rs}}{\text{.}}\left( {\frac{{80}}{{100}} \times 2x} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{8x}}{5}. \cr & {\text{Profit = Rs}}{\text{.}}\left( {\frac{{8x}}{5} - \frac{{10x}}{{11}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{38x}}{{55}}. \cr & \therefore {\text{ Profit }}\% \cr & {\text{ = }}\left( {\frac{{38x}}{{55}} \times \frac{{11}}{{10x}} \times 100} \right)\% \cr & = 76\% \cr}$$

Explanation:-

$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{. be Rs}}{\text{.100}}{\text{.}} \cr & {\text{Then, }} \cr & {\text{marked price = Rs}}{\text{.130}}{\text{.}} \cr & {\text{Selling Price}} \cr & {\text{ = }}\left( {100 - \frac{{25}}{4}} \right)\% {\text{ of Rs}}{\text{.130}} \cr & {\text{ = Rs}}{\text{.}}\left( {\frac{{375}}{{400}} \times 130} \right) \cr & = {\text{Rs}}{\text{.121}}{\text{.875}}{\text{.}} \cr & \therefore {\text{ Profit }}\% \cr & {\text{ = }}\left( {121.875 - 100} \right)\% \cr & {\text{ = 21}}{\text{.875}}\% \cr & {\text{ = }}\frac{{21875}}{{1000}}{\text{ }}\% \cr & {\text{ = 21}}\frac{7}{8}\% . \cr}$$

Explanation:-

Let the number of bad apples = x
Cost price of (240 - x) apples = Rs. 3.50 × (240 - x)
According to the question,
⇒ 3.50 × (240 - x) - 600 = 198
⇒ x = 12
So, % of apples thrown away are $$\eqalign{ & x\% = \frac{{12}}{{240}} \times 100\% \cr & \,\,\,\,\,\,\,\,\,\, = 5\% \cr}$$
Alternate :
Selling price of apples
= 600 + 198 = 798
Number of apples sold $$\eqalign{ & = \frac{{798}}{{3.50}} = 228 \cr & \% {\text{ of apples thrown}} \cr & {\text{ = }}\frac{{240 - 228}}{{240}} \times 100 \cr & = \frac{{12}}{{240}} \times 100 \cr & = 5\% \cr}$$

Explanation:-

According to the question,
Cost price of the radio = Rs. 600
5% of cost price is charged $$\eqalign{ & = \frac{5}{{100}} \times 600 \cr & = {\text{Rs}}{\text{. 30}} \cr}$$ ∴ Total cost price = 60 + 30 = Rs. 630
To gain 15% then selling price $$\eqalign{ & = 630 + \frac{{15}}{{100}} \times 630 \cr & = {\text{Rs}}{\text{. 724}}{\text{.50}} \cr}$$

Explanation:-

Let Cost price be Rs. 100
Then,
Marked price = Rs. 125
Selling price = 84% of Rs. 125 $$\eqalign{ & {\text{ = Rs}}{\text{.}}\left( {\frac{{84}}{{100}} \times 125} \right) \cr & = {\text{Rs}}{\text{.105}}{\text{.}} \cr}$$ ∴ Profit % = (105 - 100) % = 5%

Explanation:-

According to the question,
Pen × Profit (%) = Total Profit
Total 150 pens × 15 = 2250
50 × 10 = 500
100 × a = 1750
a = 17.5
∴ Remaining profit % of pen = 17.5%