## Discount

#### Discount

1. A shopkeeper offers 10% discount on the marked price of his articles and still makes a profit of 20%. What is the actual cost of the article marked ₹ 500 for him ?
1. ₹ 440
2. ₹ 425
3. ₹ 400
4. ₹ 375

1. Given that , marked price = ₹ 500
Discount = 10% and profit = 20%
Let the cost price of article be p.

 ∴  500 × 90 = 120 × p 100 100

 ⇒  450 = 6p 5

 ⇒  p = 450 × 5 = ₹ 375 6

Second method :
C.P. = ? , M.P. = ₹ 500, r = 20%, D = 10%
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: D

Given that , marked price = ₹ 500
Discount = 10% and profit = 20%
Let the cost price of article be p.

 ∴  500 × 90 = 120 × p 100 100

 ⇒  450 = 6p 5

 ⇒  p = 450 × 5 = ₹ 375 6

Second method :
C.P. = ? , M.P. = ₹ 500, r = 20%, D = 10%
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

 500 = 100 + 20 C.P. 100 − 10

 C.P. = 500 × 90 = ₹ 375 120

1. The cost of manufacturing an article was ₹ 900. The trader wants to gain 25% after giving a discount of 10%. The marked price must be :
1. ₹ 1500
2. ₹ 1250
3. ₹ 1200
4. ₹ 1000

1. Here , CP of article = ₹ 900 , discount = 10%
∴  After 25% gain , S.P. of article = 125% of 900

 S.P. of article = 900 × 125 = ₹ 1125 100

Let the marked price be y

##### Correct Option: B

Here , CP of article = ₹ 900 , discount = 10%
∴  After 25% gain , S.P. of article = 125% of 900

 S.P. of article = 900 × 125 = ₹ 1125 100

Let the marked price be y
∴  90% of y = 1125
 ⇒  y = 1125 × 100 = ₹ 1250 90

1. A shopkeeper buys an article for ₹ 180. He wishes to gain 20% after allowing a discount of 10% on the marked price to the customer. The marked price will be
1. ₹ 210
2. ₹ 240
3. ₹ 270
4. ₹ 300

1. Given in question , CP of article = ₹ 180

 After 20% gain , SP = 180 × 120 = ₹ 216 100

discount = 10%
∴  ( 100 - 10 )% = 216
⇒  90% = 216

##### Correct Option: B

Given in question , CP of article = ₹ 180

 After 20% gain , SP = 180 × 120 = ₹ 216 100

discount = 10%
∴  ( 100 - 10 )% = 216
⇒  90% = 216
 100% = 216 × 100 = ₹ 240 90

Hence , The marked price is ₹ 240 .

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. 30%
2.  33 1 % 3
3.  34 2 % 3
4. 35%

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

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. 20%
2. 24%
3. 25%
4. 28%

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