## Discount

#### Discount

1. The marked price of a radio is ₹ 4,800. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain per cent will be
1. 18%
2. 20%
3. 22%
4. 25%

1. Here , marked price of a radio = ₹ 4,800 , discount = 10% and gains = 8%
Let CP of radio be Rs. y.
According to the question,

 108y = 4800 × 90 = 4320 100 100

 ⇒  y = 4320 × 100 = ₹ 4000 108

Gain = 4800 - 4000 = ₹ 800
If no discount is allowed,then
 Gain percent = 800 × 100 = 20% 4000

Second method :
Given Here , M.P. = ₹ 4800, D = 10%, r = 8%
With the help of given formula ,
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: B

Here , marked price of a radio = ₹ 4,800 , discount = 10% and gains = 8%
Let CP of radio be Rs. y.
According to the question,

 108y = 4800 × 90 = 4320 100 100

 ⇒  y = 4320 × 100 = ₹ 4000 108

Gain = 4800 - 4000 = ₹ 800
If no discount is allowed,then
 Gain percent = 800 × 100 = 20% 4000

Second method :
Given Here , M.P. = ₹ 4800, D = 10%, r = 8%
With the help of given formula ,
 M.P. = 100 + r C.P. 100 − D

 4800 = 100 + 8 C.P. 100 − 10

 C.P. = 4800 × 90 = 4000 108

 Gain % (without discount) = 4800 − 4000 × 100 4000

 Gain % = 800 × 100 = 20% 4000

1. After allowing a discount of 16%, there was still a gain of 5%. Then the percentage of marked price over the cost price is
1. 15%
2. 18%
3. 21%
4. 25%

1. Let the C.P. of article be ₹ 100 and its marked price be y.
Discount = 16% and gain = 5%

 ∴  y × 84 = 105 100

 ⇒  y = 105 × 100 = 125 84

Difference = 125 - 100 = 25
∵ C.P. of article = ₹ 100
∴  Required percentage = 25%
Second method to solve this question :
Here, r = 5% , D = 16%
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: D

Let the C.P. of article be ₹ 100 and its marked price be y.
Discount = 16% and gain = 5%

 ∴  y × 84 = 105 100

 ⇒  y = 105 × 100 = 125 84

Difference = 125 - 100 = 25
∵ C.P. of article = ₹ 100
∴  Required percentage = 25%
Second method to solve this question :
Here, r = 5% , D = 16%
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

 M.P. = 100 + 5 = 105 C.P. 100 − 16 84

 Required Percentage = 105 − 84 × 100 = 25% 84

1. A trader sells his goods at a discount of 20%. He still makes a profit of 25%. If he sells the goods at the marked price only, his profit will be
1. 56.25%
2. 25.56%
3. 50.25%
4. 54.25%

1. Let the marked price = ₹ 100
∴  S.P after discount of 20% = ₹ 80
Profit = 25%

 ∴  CP = ₹ 100 ×80 = ₹ 64 125

Profit after selling on marked price= 100 – 64 = ₹ 36
 ∴  Gain % = 36 × 100 = 56.25% 64

Second method to solve this question :
Here, D = 20%,r = 25%
Let, M.P. be ₹ 100
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: A

Let the marked price = ₹ 100
∴  S.P after discount of 20% = ₹ 80
Profit = 25%

 ∴  CP = ₹ 100 ×80 = ₹ 64 125

Profit after selling on marked price= 100 – 64 = ₹ 36
 ∴  Gain % = 36 × 100 = 56.25% 64

Second method to solve this question :
Here, D = 20%,r = 25%
Let, M.P. be ₹ 100
 M.P. = 100 + r C.P. 100 − D

 100 = 100 + 25 C.P. 100 − 20

 C.P. = 100 × 80 = ₹ 64 125

Profit = 100 – 64 = 36
 Gain % = 36 × 100% = 56.25% 64

1. In order to maintain the price line a trader allows a discount of 10% on the marked price of an article. However, he still makes a profit of 17% on the cost price. Had he sold the article at the marked price, he would have earned a profit per cent of
1. 30%
2. 32%
3. 33%
4. 35%

1. Given in question , discount = 10%
Let the marked price be ₹ 100.
∴  S.P. = 90% of 100 = ₹ 90
Profit = 17%

 C.P.= ₹ 90 × 100 117

 C.P. = ₹ 1000 13

If no discount is allowed, S.P. = ₹ 100
 Profit = ₹ 100 − 1000 = ₹ 300 13 13

 ∴  Profit % = ( 300 / 13 ) × 100 = 30% ( 1000 / 13 )

Second method :
Here, D = 10%, r = 17%,
Let the M.P. = ₹ 100
With the help of given formula ,
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: A

Given in question , discount = 10%
Let the marked price be ₹ 100.
∴  S.P. = 90% of 100 = ₹ 90
Profit = 17%

 C.P.= ₹ 90 × 100 117

 C.P. = ₹ 1000 13

If no discount is allowed, S.P. = ₹ 100
 Profit = ₹ 100 − 1000 = ₹ 300 13 13

 ∴  Profit % = ( 300 / 13 ) × 100 = 30% ( 1000 / 13 )

Second method :
Here, D = 10%, r = 17%,
Let the M.P. = ₹ 100
With the help of given formula ,
 M.P. = 100 + r C.P. 100 − D

 100 = 100 + 17 C.P. 100 − 10

 100 = 117 C.P. 90

 C.P. = 100 × 90 = 1000 117 13

Profit = S.P. – C.P.
 Profit = 100 − 1000 13

 Profit = Rs. 300 13

 Profit % = ( 300 / 13 ) × 100 = 30% ( 1000 / 13 )

1. The price that Akbar should mark on a pair of shoes which costs him ₹ 1,200 to gain 12% after allowing a discount of 16% (in rupees) is
1. 1,344
2. 1,433
3. 1,600
4. 1,500

1. Given that , Cost price of pair of shoes = ₹ 1,200 , Gain = 12%
Let the marked price be y.

 ∴  y × 84 = 1200 × 112 100 100

 = y × 80 = 112 × 12 400

 ⇒  y = 112 × 1200 = ₹ 1600 84

Second method :
Given Here , C.P. = ₹ 1200, r = 12%, D = 16%
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: C

Given that , Cost price of pair of shoes = ₹ 1,200 , Gain = 12%
Let the marked price be y.

 ∴  y × 84 = 1200 × 112 100 100

 = y × 80 = 112 × 12 400

 ⇒  y = 112 × 1200 = ₹ 1600 84

Second method :
Given Here , C.P. = ₹ 1200, r = 12%, D = 16%
 M.P. = 100 + r C.P. 100 − D

 M.P. = 100 + 12 1200 100 − 16

 M.P. = 112 × 1200 = ₹ 1600 84