## Discount

#### Discount

1. The marked price of an electric iron is ₹ 690. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain percent would be

1. Given in question , Marked price = ₹ 690
∴  Discount = 10%

 SP = 690 × 90 = ₹ 621 100

Profit = 8%
 ∴  CP = 621 × 100 = ₹ 575 108

Profit without discount = 690 – 575 = ₹ 115
 Profit percent = 115 × 100 = 20% 575

Using the given formula , we can find required answer :
Here, r = 10%, R = 20%
 Required percentage = (r + R) × 100% 100 − r

 Required percentage = 10 + 20 × 100% 100 − 10

 Required percentage = 30 × 100% 90

 Required percentage = 33 1 % 3

Gain = S.P. - C.P. = 480 − 400 = ₹ 80
 Gain % = Gain × 100 (without discount) C.P.

 = 80 × 100 = 20% 400

We can find required answer with the help of given formula :
Here, M.P. = ₹ 690 , D = 10% , r = 8%
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: A

Given in question , Marked price = ₹ 690
∴  Discount = 10%

 SP = 690 × 90 = ₹ 621 100

Profit = 8%
 ∴  CP = 621 × 100 = ₹ 575 108

Profit without discount = 690 – 575 = ₹ 115
 Profit percent = 115 × 100 = 20% 575

Using the given formula , we can find required answer :
Here, r = 10%, R = 20%
 Required percentage = (r + R) × 100% 100 − r

 Required percentage = 10 + 20 × 100% 100 − 10

 Required percentage = 30 × 100% 90

 Required percentage = 33 1 % 3

Gain = S.P. - C.P. = 480 − 400 = ₹ 80
 Gain % = Gain × 100 (without discount) C.P.

 = 80 × 100 = 20% 400

We can find required answer with the help of given formula :
Here, M.P. = ₹ 690 , D = 10% , r = 8%
 M.P. = 100 + r C.P. 100 − D

 690 = 100 + 8 C.P. 100 − 10

 690 = 108 C.P. 90

 C.P. = 690 × 90 = ₹ 575 108

 Gain % (without discount) = 690 × 575 × 100% 575

 Gain % = 115 × 100% = 20% 575

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

1. Given Here , marked price = ₹ 880
SP of article = (100 – 20)% of 880 = 80% of 880
Let CP be y
Again, 110% of y = 704

 y = 704 × 100 = ₹ 640 110

∴  Original cost = ₹ 640
We can find required answer with the help of given formula :
Here, r = 10%, D = 20%, M.P. = ₹ 880, C.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: B

Given Here , marked price = ₹ 880
SP of article = (100 – 20)% of 880 = 80% of 880
Let CP be y
Again, 110% of y = 704

 y = 704 × 100 = ₹ 640 110

∴  Original cost = ₹ 640
We can find required answer with the help of given formula :
Here, r = 10%, D = 20%, M.P. = ₹ 880, C.P. = ?
 M.P. = 100 + r C.P. 100 − D

 880 = 100 + 10 C.P. 100 − 20

 880 = 110 C.P. 80

 C.P. = 880 × 80 110

C.P. = ₹ 640

1. By giving a discount of 10% on the marked price of ₹ 1100 of a cycle, a dealer gains 10%. The cost price of the cycle is :

1. Given that , discount = 10% and marked price of cycle = ₹ 1100
Selling Price = ₹ (1100 – 10% of 1100) = ₹ (1100 – 110) = 990
Let the cost price = y
According to question ,
∴  y + 10% of y = 990

 ⇒ 11y = 990 10

 ⇒  y = 990 × 10 = ₹ 900 11

Second method to solve this question :
Here, r = 10% , D = 10% , M.P. = ₹ 1100 , C.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: B

Given that , discount = 10% and marked price of cycle = ₹ 1100
Selling Price = ₹ (1100 – 10% of 1100) = ₹ (1100 – 110) = 990
Let the cost price = y
According to question ,
∴  y + 10% of y = 990

 ⇒ 11y = 990 10

 ⇒  y = 990 × 10 = ₹ 900 11

Second method to solve this question :
Here, r = 10% , D = 10% , M.P. = ₹ 1100 , C.P. = ?
 M.P. = 100 + r C.P. 100 − D

 1100 = 100 + 10 C.P. 100 − 10

 C.P. = 1100 × 90 = ₹ 900 110

1.  The marked price of an article is ₹ 200. A discount of 12 1 % is allowed on the marked price 2
and a profit of 25% is made. The cost price of the article is :

1. Given that , marked price of an article = ₹ 200

 Discount = 12 1 % = 25 % 2 2

After discount , S.P. = ₹ 200 × 87.5 = ₹ 175
Gain % = 25%
 Required C.P. = ₹ 100 × 175 = ₹ 140 125

Using the given formula :
Here, r = 25% , D = 12.5% , M.P. = ₹ 200 , C.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: D

Given that , marked price of an article = ₹ 200

 Discount = 12 1 % = 25 % 2 2

After discount , S.P. = ₹ 200 × 87.5 = ₹ 175
Gain % = 25%
 Required C.P. = ₹ 100 × 175 = ₹ 140 125

Using the given formula :
Here, r = 25% , D = 12.5% , M.P. = ₹ 200 , C.P. = ?
 M.P. = 100 + r C.P. 100 − D

 200 = 100 + 25 C.P. 100 − 12.5

 C.P. = 200 × 87.5 125

C.P. = ₹ 140

1. A trader wishes to gain 20% after allowing 10% discount on the marked price to his customers. At what per cent higher than the cost price must he marks his goods ?

1. Let the CP be ₹ 100. Then SP on 20% gain = ₹ 120
Let the marked price be y.
Then, ( 100 - 10 )% of y = ₹ 120
⇒ 90% of y = ₹ 120

 ⇒  y = 120 × 100 = 400 90 3

##### Correct Option: B

Let the CP be ₹ 100. Then SP on 20% gain = ₹ 120
Let the marked price be y.
Then, ( 100 - 10 )% of y = ₹ 120
⇒ 90% of y = ₹ 120

 ⇒  y = 120 × 100 = 400 90 3

 y = 133 1 3

 It is 33 1 % higher than the CP. 3