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

Exercise 8B

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Q1 | Ex-8B | Class 8 | S.Chand | Composite maths | Profit,Loss and Discount |Ch-8 | myhelper

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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

 

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Q2 | Ex-8B | Class 8 | S.Chand | Composite maths | Profit,Loss and Discount |Ch-8 | myhelper

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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 %

 

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Q3 | Ex-8B | Class 8 | S.Chand | Composite maths | Profit,Loss and Discount |Ch-8 | myhelper

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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

 

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Q4 | Ex-8B | Class 8 | S.Chand | Composite maths | Profit,Loss and Discount |Ch-8 | myhelper

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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

 

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Q5 | Ex-8B | Class 8 | S.Chand | Composite maths | Profit,Loss and Discount |Ch-8 | myhelper

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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 =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 %

 

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Q6 | Ex-8B | Class 8 | S.Chand | Composite maths | Profit,Loss and Discount |Ch-8 | myhelper

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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 = SP - CP

16=160-CP

C.P = 160-16

C.P = 144

$\text{Gain}\%=\dfrac{\text{gain}}{C.P}\times 100$

$\text{Gain}\%=\dfrac{16}{144}\times 100$

$=11\dfrac{1}{9}\%$

 

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Q7 | Ex-8B | Class 8 | S.Chand | Composite maths | Profit,Loss and Discount |Ch-8 | myhelper

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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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