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S.chand books class 8 maths solution chapter Profit,Loss and Discount Exercise 8B

Exercise 8B


QUESTION 1

The marked price of a saree is ₹ 3800 . The shopkeeper offers a discount of 15% during sale time . What is the selling price of saree ?

Sol :

Given : M.P = 3800 and Discount = 15%

\text{S.P}=\dfrac{100-Discount\%}{100}\times \text{M.P}

=\dfrac{100-15}{100}\times 3800

=\dfrac{85}{100}\times 3800

= 3,230

 


QUESTION 2

The marked price of a shirt is ₹ 270 and it is available at ₹ 237.60 after discount . What is the rate of discount ?

Sol :

At , first we have to find discount

Discount = 270 – 237.60

= 32.4

We know that \text{Discount}\%=\dfrac{\text{discount}}{\text{M.P}}\times 100

=\dfrac{32.4}{270}\times 100

= 12 %

 


QUESTION 3

A person purchased a shirt for ₹ 600 , after a discount of 20% was offered on the market price of the shirt ?

Sol :

Given : Discount % = 20 %

let’s find M.P of shirt

\text{M.P}=\dfrac{\text{S.P}}{100-Discount\%}\times 100

=\dfrac{600}{100-20}\times 100

=\dfrac{600}{80}\times 100

= 750

 


QUESTION 4

A shopkeeper earns a profit of 10% after allowing a discount of 20% on the market price . Find the cost price of the article whose marked price is ₹ 880.

Sol :

Given : Discount % = 20 % , Profit = 10 % , M.P = 880

\text{S.P}=\dfrac{100-\text{Discount}\%}{100}\times \text{M.P}

=\dfrac{100-20}{100}\times 880

=\dfrac{80}{100}\times 880

S.P = 704

We know Profit = S.P – C.P and \text{Profit}\%=\dfrac{\text{Profit}}{\text{C.P}}\times 100 or \text{Profit}\%=\dfrac{\text{S.P - C.P}}{\text{C.P}}\times 100

\text{Profit}\%=\left(\dfrac{\text{S.P}}{\text{C.P}} - \dfrac{\text{C.P}}{\text{C.P}} \right)\times 100

\text{Profit}\%=\left(\dfrac{\text{S.P}}{\text{C.P}} - 1 \right)\times 100

10=\left(\dfrac{704}{\text{C.P}} - 1 \right)\times 100

\dfrac{10}{100}=\dfrac{704}{\text{C.P}} - 1

\dfrac{1}{10}+1=\dfrac{704}{\text{C.P}}

\dfrac{1+10}{10}=\dfrac{704}{\text{C.P}}

\dfrac{11}{10}=\dfrac{704}{\text{C.P}}

\text{C.P}=\dfrac{704\times 10}{11}

C.P = 640

 


QUESTION 5

A shopkeeper marks his goods 20% above the cost price , but allows 30% discount for cash . What is his net loss percent ?

Sol :

According to question , M.P = \text{C.P} +  (20% of C.P)

\text{M.P}=\text{C.P} + \dfrac{20}{100}\times \text{C.P}

\text{M.P}=\text{C.P} + \dfrac{\text{C.P}}{5}

\text{M.P}=\dfrac{6}{5}\times \text{C.P}

Also ,

\text{S.P}=\dfrac{100-\text{Discount}\%}{100}\times \text{M.P}

\text{S.P}=\dfrac{100-30}{100}\times \dfrac{6}{5}\times \text{C.P}

\text{S.P}=\dfrac{70}{100}\times \dfrac{6}{5}\times \text{C.P}

\text{S.P}=\dfrac{7}{5}\times \dfrac{3}{5}\times \text{C.P}

\text{S.P}=\dfrac{21}{25}\times \text{C.P}

And putting values of S.P in below formula , we get

\text{C.P}=\left(\dfrac{100}{100-\text{loss}\%}\right)\times \text{S.P}

\text{C.P}=\left(\dfrac{100}{100-\text{loss}\%}\right)\times \dfrac{21}{25}\times \text{C.P}

\text{C.P}\times \dfrac{25}{21}\times \dfrac{1}{\text{C.P}}=\dfrac{100}{100-\text{loss}\%}

\dfrac{25}{21}=\dfrac{100}{100-\text{loss}\%}

2100=25(100-\text{loss }\%)

\dfrac{2100}{25}=(100-\text{loss }\%)

84=100-\text{loss }\%

\text{loss }\%=100-84

Loss % = 16 %

 


QUESTION 6

The marked price of a T-shirt is ₹ 200 . After allowing a discount of 20% on the marked price , the shopkeeper makes a profit of ₹ 16 . Find the gain percent ?

Sol :

Lets find Selling Price of t-shirt

\text{S.P}=\dfrac{100-\text{Discount}\%}{100}\times \text{M.P}

=\dfrac{100-20}{100}\times 200

=\dfrac{80}{100}\times 200

S.P = 160

Profit = C.P – S.P

16 = C.P – 160

C.P = 16 + 160

C.P = 176

\text{Gain}\%=\dfrac{16}{176}\times 100

=\dfrac{1600}{176}=\dfrac{800}{88}=\dfrac{400}{44} =\dfrac{200}{22}=\dfrac{100}{11}=9\dfrac{1}{11}

 


QUESTION 7

A shopkeeper allows a discount of 10% to his customers and still gains 20% . Find the marked price of the article which cost ₹ 450 .

Sol :

We know that

\text{C.P}=\left(\dfrac{100}{100+\text{Gain\%}}\right)\times \text{S.P}

450=\left(\dfrac{100}{100+20}\right)\times \text{S.P}

450=\dfrac{100}{120}\times \text{S.P}

\text{S.P}=\dfrac{450\times 120}{100}

S.P = 540

Putting value of S.P in below formula

\text{M.P}=\dfrac{\text{S.P}}{100-\text{Discount}\%}\times 100

\text{M.P}=\dfrac{540}{100-10}\times 100

=\dfrac{540}{90}\times 100

M.P = 600

 


 

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