## Discount

#### Discount

1. What price should a shopkeeper mark on an article costing him ₹ 200 to gain 35% after allowing a discount of 25% ?
1. ₹ 270
2. ₹ 300
3. ₹ 330
4. ₹ 360

1. Let the marked price be p.

 ∴ p × 75 = 200 × 135 100 100

 ⇒  p = 200 × 135 = ₹ 360 75

2nd method to solve this question.
Here, r = 25%, R = 35%,
C.P. = ₹ 200
 Marked price = Rs. 200 + 200 × r + R × 100 % 100 − r

##### Correct Option: D

Let the marked price be p.

 ∴ p × 75 = 200 × 135 100 100

 ⇒  p = 200 × 135 = ₹ 360 75

2nd method to solve this question.
Here, r = 25%, R = 35%,
C.P. = ₹ 200
 Marked price = Rs. 200 + 200 × r + R × 100 % 100 − r

 = 200 + 200 × 25 + 35 % × 100 100 − 25

 = 200 + 200 × 60 × 100% 75

 = 200 + 200 × 20 × 4 100

Hence Marked price = 200 + 160 = ₹ 360

1. A tradesman marks his goods at 25% above its cost price and allows purchasers a discount of
 12 1 % for cash payment. The profit, he thus makes, is 2
1.  9 3 % 8
2.  9 1 % 2
3.  8 1 % 2
4.  8 3 % 8

1. Let the cost price of article = 100
∴  Marked price = ₹ 125

 SP of the article = 100 − 25 % of 125 2

 SP of the article = 175 % of 125 2

 SP of the article = 125 × 175 = 875 2 × 100 8

 S.P. = ₹ 109 3 8

 ∴  Gain percent = 109 3 − 100 = 9 3 % 8 8

2nd method to solve this question.
Here, r = 25%,
 r1 = 12 1 % = 12.5 % 2

##### Correct Option: A

Let the cost price of article = 100
∴  Marked price = ₹ 125

 SP of the article = 100 − 25 % of 125 2

 SP of the article = 175 % of 125 2

 SP of the article = 125 × 175 = 875 2 × 100 8

 S.P. = ₹ 109 3 8

 ∴  Gain percent = 109 3 − 100 = 9 3 % 8 8

2nd method to solve this question.
Here, r = 25%,
 r1 = 12 1 % = 12.5 % 2

 Profit % = r × (100 − r1) − r1 100

 Profit % = 25 × (100 − 12.5) − 12.5 100

 Profit % = 25 × 87.5 − 12.5 100

Profit % = 21.875 – 12.5 = 9.375
 Required Profit % = 9 3 % 8

1. A seller marks his goods 30% above their cost price but allows 15% discount for cash payment. His percentage of profit when sold in cash is
1. 10.5%
2. 15%
3. 9%
4. 8.5%

1. Let the C.P. be ₹ 100
∴  Marked price = ₹ 130

 S.P. = 85% of ₹ 130 = ₹ 85 × 130 = ₹ 110.5 100

∴  Gain percent = 10.5%
2nd method to solve this question.
Here, r = 30%, r1 = 15%
 Profit % = r × (100 − r1) − r1 100

##### Correct Option: A

Let the C.P. be ₹ 100
∴  Marked price = ₹ 130
S.P. = 85% of ₹ 130

 = ₹ 85 × 130 = ₹ 110.5 100

∴  Gain percent = 10.5%
2nd method to solve this question.
Here, r = 30%, r1 = 15%
 Profit % = r × (100 − r1) − r1 100

 Profit % = 30 × (100 − 15) − 15 100

 Profit % = 30 × 85 − 15 100

Required Profit % = 25.5 – 15 = 10.5%

1. A shopkeeper marks his sarees at 20% above the cost price and allows the purchaser a discount of 10% for cash buying. What profit percent does he make?
1. 18%
2. 12%
3. 10%
4. 8%

1. As we know that ,

 Gain % = a − b − a × b 100

 Gain % = 20 − 10 − 20 × 10 100

2nd method to solve this question .
Here, r = 20%, r1 = 10%

##### Correct Option: D

As we know that ,

 Gain % = a − b − a × b 100

 Gain % = 20 − 10 − 20 × 10 100

2nd method to solve this question .
Here, r = 20%, r1 = 10%
 Profit or loss = r × (100 − r1) − r1 100

 Profit or loss = 20 × (100 − 10) − 10 100

Required Profit or loss = 18 – 10 = 8% profit.

1. A shopkeeper marks his goods 20% above cost price, but allows 30% discount for cash. His net loss is :
1. 8%
2. 10%
3. 16%
4. 20%

1. Let the cost price be p Mark Price

 = 1 + 20 p = 1.2p 100

 Cash price = 1 − 30 1.2p 100

= 0.7 × 1.2p = 0.84p
Net Loss = p – 0.84p = 0.16p
 ∴  Net loss% = 0.16p × 100 = 16% p

2nd method to solve this question.
Here, r = 20%, r1 = 30%
 Profit or loss = r ×(100 − r1) −r1 100

##### Correct Option: C

Let the cost price be p Mark Price

 = 1 + 20 p = 1.2p 100

 Cash price = 1 − 30 1.2p 100

= 0.7 × 1.2p = 0.84p
Net Loss = p – 0.84p = 0.16p
 ∴  Net loss% = 0.16p × 100 = 16% p

2nd method to solve this question.
Here, r = 20%, r1 = 30%
 Profit or loss = r ×(100 − r1) −r1 100

 Profit or loss = 20 × (100 − 30) − 30 100

Profit or loss= 14 – 30 = –16%
Required Profit or loss = 16% loss