## Discount

#### Discount

1. A shopkeeper allows a discount of 12.5 % on the marked price of a certain article and makes a profit of 20 %. If the article costs the shopkeeper ₹ 210, then the marked price of the article will be
1. ₹ 387
2. ₹ 350
3. ₹ 386
4. ₹ 288

1. Let Marked price of article = ₹ p

 ∴ p × (100 − 12.5) = 210 × 120 100 100

2nd method to solve this question.
Here,R= 20%, D = 12.5%,
C.P. = ₹ 210, M.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: D

Let Marked price of article = ₹ p

 ∴ p × (100 − 12.5) = 210 × 120 100 100

⇒  p × 87.5 = 210 ×120
 ⇒  p = 210 × 120 = ₹ 288 87.5

2nd method to solve this question.
Here,R= 20%, D = 12.5%,
C.P. = ₹ 210, M.P. = ?
 M.P. = 100 + r C.P. 100 − D

 M.P. = 100 + 20 210 100 − 12.5

 M.P. = 120 × 210 87.5

Hence Marked Price = ₹ 288

1. The cost price of a table is ₹ 3,200. A merchant wants to make 25 % profit by selling it. At the the time of sale he declares a discount of 20 % on the marked price. The marked price (in ₹) is
1. 5,000
2. 6,000
3. 4,000
4. 4,500

1. Let the marked price of table be ₹ p.

 ∴ p × 80 = 3200 × 125 100 100

2nd method to solve this question.
Here, r = 25%, D = 20%,
C.P. = ₹ 3200, M.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: A

Let the marked price of table be ₹ p.

 ∴ p × 80 = 3200 × 125 100 100

⇒  p × 80 = 3200 × 125
 ⇒  p = 3200 × 125 = ₹ 5000 80

2nd method to solve this question.
Here, r = 25%, D = 20%,
C.P. = ₹ 3200, M.P. = ?
 M.P. = 100 + r C.P. 100 − D

 M.P. = 100 + 25 3200 100 − 20

 M.P. = 125 × 3200 = ₹ 5000 80

1. Jasmine allows 4% discount on the marked price of her goods and still earns a profit of 20%. What is the cost price of a shirt if its marked price is ₹ 850?
1. ₹ 650
2. ₹ 720
3. ₹ 700
4. ₹ 680

1. Let Cost price of the shirt = ₹ p

 ∴  p × 120 = 850 × 96 100 100

2nd method to solve this question.
Here r = 20%, D = 4%,
M.P. = ₹ 850, C.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: D

Let Cost price of the shirt = ₹ p

 ∴  p × 120 = 850 × 96 100 100

⇒  p × 120 = 850 × 96
 ⇒  p = 850 × 96 = ₹ 680 120

2nd method to solve this question.
Here r = 20%, D = 4%,
M.P. = ₹ 850, C.P. = ?
 M.P. = 100 + r C.P. 100 − D

 850 = 100 + 20 C.P. 100 − 4

 C.P. = 850 × 96 120

C.P. = ₹ 680

1. How much percent above the cost price should a shopkeeper mark his goods so as to earn a profit of 32% after allowing a discount of 12% on the marked price ?
1. 50%
2. 40%
3. 60%
4. 45%

1. Let the C.P. be ₹ 100 and the marked price be ₹ p.

 ∴  p × 88 = 132 100

2nd method to solve this question.
Here, Gain % = 32%,, r1 = 12%, r = ?
 Gain % = r × (100 − r1) − r1 100

##### Correct Option: A

Let the C.P. be ₹ 100 and the marked price be ₹ p.

 ∴  p × 88 = 132 100

 ⇒  p = 132 × 100 88

= 150 i.e., more by 50%
∴  Required percentage = 50%
2nd method to solve this question.
Here, Gain % = 32%,, r1 = 12%, r = ?
 Gain % = r × (100 − r1) − r1 100

 32 = r × (100 − 12) − 12 100

 44 = r × 88 100

r = 50%

1. To gain 8% after allowing a discount of 10%, by what percent cost price should be hiked in the list price ?
1. 9%
2. 11%
3. 18%
4. 20%

1. Let the cost price be ₹ 100 and marked price be p.

 ∴ p × 90 = 108 100

 ⇒ 9p = 108 10

2nd method to solve this question.
Here, Gain % = 8%,, r1 = 10%, r = ?
 Gain % = r ×(100 − r1) − r1 100

##### Correct Option: D

Let the cost price be ₹ 100 and marked price be p.

 ∴ p × 90 = 108 100

 ⇒ 9p = 108 10

 ⇒  p = 108 × 10 = 120 9

Required Percent = 20%
2nd method to solve this question.
Here, Gain % = 8%,, r1 = 10%, r = ?
 Gain % = r ×(100 − r1) − r1 100

 8 = r × (100 − 10) − 10 100

 8 = r × 90 − 10 9

 18 = r × 9 = 20% 9