## Discount

#### Discount

1. A discount of 14% on the marked price of an article is allowed and then the article is sold for ₹ 387. The marked price of the article is
1. ₹ 450
2. ₹ 427
3. ₹ 500
4. ₹ 440

1. Here , SP of article = ₹ 387 , discount = 14%
Let the marked price be y
∴  ( 100 - 14 )% of y = 387
⇒ 86% of y = 387

 ∴  y = 387 × 100 = ₹ 450 86

We can find required answer with the help of given formula :
Here, D = 14%, S.P. = 387, M.P. = ?
 M.P. = S.P. × 100 100 − D

##### Correct Option: A

Here , SP of article = ₹ 387 , discount = 14%
Let the marked price be y
∴  ( 100 - 14 )% of y = 387
⇒ 86% of y = 387

 ∴  y = 387 × 100 = ₹ 450 86

We can find required answer with the help of given formula :
Here, D = 14%, S.P. = 387, M.P. = ?
 M.P. = S.P. × 100 100 − D

 = 387 × 100 100 − 14

 = 38700 = ₹ 450 86

1. A man buys an article for ₹ 80 and marks it at ₹ 120. He then allows a discount of 40%. What is the loss or gain percent ?
1. 12% gain
2. 12% loss
3. 10% gain
4. 10% loss

1. Given that , CP of article = ₹ 80 and marked price = ₹ 120

 Discount = 120 × 40 = ₹ 48 100

∴  S.P. = ₹ (120 – 48) = ₹ 72
Loss = 80 – 72 = ₹ 8
 ∴  Loss % = 8 × 100 = 10% 80

Second method to solve this question :
Here, C.P. = Rs. 80, M.P. = Rs. 120, D = 40%
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: D

Given that , CP of article = ₹ 80 and marked price = ₹ 120

 Discount = 120 × 40 = ₹ 48 100

∴  S.P. = ₹ (120 – 48) = ₹ 72
Loss = 80 – 72 = ₹ 8
 ∴  Loss % = 8 × 100 = 10% 80

Second method to solve this question :
Here, C.P. = Rs. 80, M.P. = Rs. 120, D = 40%
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

 120 = 100 + r 80 100 − 40

 3 = 100 + r 2 60

90 = 100 + r
r =–10% (–ve sign shows loss)
⇒  Loss = 10%

1. A retailer gets a discount of 40% on the printing price of an article. The retailer sells it at the printing price. His gain percent is
1. 40%
2. 55%
3.  66 2 % 3
4. 75%

1. Let the printed price of the article be ₹ 100
Discount = 40%
C.P. = ₹ (100 – 40) = ₹ 60
S.P. = ₹ 100

 ∴  Gain % = 40 × 100 60

##### Correct Option: C

Let the printed price of the article be ₹ 100
Discount = 40%
C.P. = ₹ (100 – 40) = ₹ 60
S.P. = ₹ 100

 ∴  Gain % = 40 × 100 60

 Gain % = 200 = 66 2 % 3 3

1. A fan is listed at ₹ 1,500 and a discount of 20% is offered on the list price. What additional discount must be offered to the customer now to bring the net price to ₹ 1,104 ?
1. 8%
2. 10%
3. 15%
4. 12%

1. Given that , Listed price = ₹ 1,500 and additional discount = ₹ 1,104
First discount = 20%

 Price after first discount = ₹ 1500 − 20 × 1500 100

Price after first discount = ₹ (1500 – 300) = ₹ 1200
Let the additional discount be y%
 ∴ 1200 − y × 1200 = 1104 100

##### Correct Option: A

Given that , Listed price = ₹ 1,500 and additional discount = ₹ 1,104
First discount = 20%

 Price after first discount = ₹ 1500 − 20 × 1500 100

Price after first discount = ₹ (1500 – 300) = ₹ 1200
Let the additional discount be y%
 ∴ 1200 − y × 1200 = 1104 100

⇒  1200 – 12y = 1104
⇒  12y = 1200 – 1104 = 96
 ⇒  y = 96 = 8% 12

1. A retailer buys 40 pens at the marked price of 36 pens from a wholesaler. If he sells these pens giving a discount of 1%, what is the profit percent?
1. 9%
2. 10%
3.  10 1 % 9
4. 11%

1. Let the marked price of each pen be y.
Total cost price of 40 pens = Total marked price of 36 pens = ₹ 36y
Selling price of 1 pen after 1% discount = (1 – 0.01)y = ₹ 0.99y
Selling price of 40 pens = 40 × 0.99y = ₹ 39.6y
Profit = SP - CP = 39.6y - 36y = ₹ 3.6y

 Profit % = 3.6 y × 100 36y

##### Correct Option: B

Let the marked price of each pen be y.
Total cost price of 40 pens = Total marked price of 36 pens = ₹ 36y
Selling price of 1 pen after 1% discount = (1 – 0.01)y = ₹ 0.99y
Selling price of 40 pens = 40 × 0.99y = ₹ 39.6y
Profit = SP - CP = 39.6y - 36y = ₹ 3.6y

 Profit % = 3.6 y × 100 36y

 Profit % = 3.6 × 100 = 10% 36