## Discount

#### Discount

1. A dealer marks his goods at 25% above the cost price and allows a discount of 10% for cash payment. His profit % is :
1. 17.5%
2. 15%
3. 12.5%
4. 20%

1. Let Cost price of article = ₹ 100
Marked price = ₹ 125

 ∴  S.P. = 125 × 90 = ₹ 112.5 100

∴  Gain = 112.5 – 100 = 12.5
⇒  Gain percent = 12.5%
2nd method to solve this question.
Here, r = 25%, r1 = 10%
 Profit % = r ×(100 − r1) − r1 100

##### Correct Option: C

Let Cost price of article = ₹ 100
Marked price = ₹ 125

 ∴  S.P. = 125 × 90 = ₹ 112.5 100

∴  Gain = 112.5 – 100 = 12.5
⇒  Gain percent = 12.5%
2nd method to solve this question.
Here, r = 25%, r1 = 10%
 Profit % = r ×(100 − r1) − r1 100

 Profit % = 25 × (100 − 10) − 10 100

 Profit % = 25 × 90 − 10 100

Required Profit % = 22.5 – 10 = 12.5%

1. The marked price is 20% higher than cost price. A discount of 20% is given on the marked price. By this type of sale, there is
1. 4% loss
2. 2% loss
3. no loss no gain
4. 4% gain

1. Let Cost price = ₹ 100
Marked price = ₹ 120

 Selling price = 120 × 80 = ₹ 96 100

2nd method to solve this question.
Here, r = 20%, r1 = 20%
 Loss % = r ×(100 − r1) − r1 100

##### Correct Option: A

Let Cost price = ₹ 100
Marked price = ₹ 120

 Selling price = 120 × 80 = ₹ 96 100

∴  Loss = 4 and loss percent = 4%
2nd method to solve this question.
Here, r = 20%, r1 = 20%
 Loss % = r ×(100 − r1) − r1 100

 Loss % = 20 × (100 − 20) − 20 100

 Loss % = 20 × 80 − 20 100

Loss % = –4% (–ve sign shows loss)
Required Loss % = 4% loss

1. A trader marks his goods 45 % above the cost price and gives a discount of 20 % on the marked price. The gain % on goods he makes is :
1. 15%
2. 14%
3. 29%
4. 16%

1. Let the C.P. of article be ₹ 100
⇒  Marked price = ₹ 145

 ⇒ S.P. = 145 × 80 = ₹ 116 100

2nd method to solve this question.
Here, r = 45%, r1 = 20%
 Gain % = r ×(100 − r1) − r1 100

##### Correct Option: D

Let the C.P. of article be ₹ 100
⇒  Marked price = ₹ 145

 ⇒ S.P. = 145 × 80 = ₹ 116 100

⇒  Profit percent = 16%
2nd method to solve this question.
Here, r = 45%, r1 = 20%
 Gain % = r × (100 − r1) − r1 100

 Gain % = 45 × (100 − 20) − 20 100

 Gain % = 3600 − 20 100

Required Gain % = 36 – 20 = 16%

1. A dealer marks his goods at 40 % above the cost price and allows a discount of 20 % on the marked price. The dealer has a
1. loss of 20 %
2. gain of 25 %
3. loss of 12 %
4. gain of 12 %

1. Let the CP of article be ₹ 100.
∴  Marked price = ₹ 140

 S.P. = 140 × 80 = ₹ 112 100

2nd Method to solve this question.
Here, r = 40%, r1 = 20%
 Required profit or loss % = r ×(100 − r1) − r1 100

##### Correct Option: D

Let the CP of article be ₹ 100.
∴  Marked price = ₹ 140

 S.P. = 140 × 80 = ₹ 112 100

∴  Gain percent = 12%
2nd Method to solve this question.
Here, r = 40%, r1 = 20%
 Required profit or loss % = r ×(100 − r1) − r1 100

 Required profit or loss % = 40 × (100 − 20) − 20 100

 Required profit or loss % = 40 × 80 −20 100

Required profit or loss % = 32 – 20 = 12% profit

1. If a shopkeeper marks the price of goods 50% more than their cost price and allows a discount of 40%, what is his gain or loss percent ?
1. Gain of 10%
2. Loss of 10%
3. Gain of 20%
4. Loss of 20%

1. Let C.P. of article = ₹ 100
Marked price = ₹ 150

 S.P. = 150 × 60 = ₹ 90 100

2nd method to solve this question.
Here, r = 50%, r1 = 40%
 His loss % = r ×(100 − r1) − r1 100

##### Correct Option: B

Let C.P. of article = ₹ 100
Marked price = ₹ 150

 S.P. = 150 × 60 = ₹ 90 100

Loss = 100 – 90 = ₹ 10 i.e. 10%
2nd method to solve this question.
Here, r = 50%, r1 = 40%
 His loss % = r ×(100 − r1) − r1 100

 Loss % = 50 × (100 − 40) − 40 100

 Loss % = 50 × 60 − 40 100

Loss % = –10% (–ve sign shows loss)
Required Loss % = 10% loss