## Discount

#### Discount

1. Marked price of an article is ₹ 275. Shopkeeper allows a discount of 5% and he gets a profit of 4.5%. The actual cost of the article is
1. ₹ 250
2. ₹ 225
3. ₹ 215
4. ₹ 210

1. Given Here , Marked price of an article = ₹ 275
profit = 4.5% , discount = 5%
Let C.P. of article be y

 ∴ y × 104.5 = 275 × 95 100 100

⇒  y × 104.5 = 275 × 95
 ⇒  y = 275 × 95 = ₹ 250 104.5

Second method :
Here , M.P. = ₹ 275, D = 5%, r = 4.5%, C.P. = ?
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: A

Given Here , Marked price of an article = ₹ 275
profit = 4.5% , discount = 5%
Let C.P. of article be y

 ∴ y × 104.5 = 275 × 95 100 100

⇒  y × 104.5 = 275 × 95
 ⇒  y = 275 × 95 = ₹ 250 104.5

Second method :
Here , M.P. = ₹ 275, D = 5%, r = 4.5%, C.P. = ?
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

 275 = 100 + 4.5 C.P. 100 − 5

 C.P. = 275 × 95 = ₹ 250 104.5

1. The marked price of a radio is ₹ 480. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain percent would be
1. 18%
2. 18.5%
3. 20.5%
4. 20%

1. Given that , The marked price of a radio = ₹ 480
If the CP of radio be y, then

 108 of y = 480 × 90 100 100

 ⇒ y × 108 = 432 100

 ⇒  y = 432 × 100 = ₹ 400 108

 Gain percent (if no discount is allowed) = 80 × 100 = 20% 400

Second method :
Here, r = 8%, D = 10%, M.P. = ₹ 480
With the help of given formula ,
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: D

Given that , The marked price of a radio = ₹ 480
If the CP of radio be y, then

 108 of y = 480 × 90 100 100

 ⇒ y × 108 = 432 100

 ⇒  y = 432 × 100 = ₹ 400 108

 Gain percent (if no discount is allowed) = 80 × 100 = 20% 400

Second method :
Here, r = 8%, D = 10%, M.P. = ₹ 480
With the help of given formula ,
 M.P. = 100 + r C.P. 100 − D

 480 = 100 + 8 C.P. 100 − 10

 C.P. = 480 × 90 = ₹ 400 108

 Gain % (without discount) = S.P. − C.P. × 100 C.P.

 Gain % = 480 − 400 × 100 400

 Gain % = 80 × 100 = 20% 400

1. A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is
1. 45 : 56
2. 45 : 51
3. 47 : 56
4. 47 : 51

1. Let the CP be 100.
After profit of 12% ,
∴  SP = 112
discount = 10%
If the marked price be y, then
90 % of y = 112

 ⇒  y = 112 × 100 = ₹ 1120 90 9

 ∴ Required ratio = 100 : 1120 9

Required ratio = 900 : 1120 = 45 : 56
Second method :
Here, r = 12%, D = 10%
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: A

Let the CP be 100.
After profit of 12% ,
∴  SP = 112
discount = 10%
If the marked price be y, then
90 % of y = 112

 ⇒  y = 112 × 100 = ₹ 1120 90 9

 ∴ Required ratio = 100 : 1120 9

Required ratio = 900 : 1120 = 45 : 56
Second method :
Here, r = 12%, D = 10%
 M.P. = 100 + r C.P. 100 − D

 M.P. = 100 + 12 C.P. 100 − 10

 M.P. = 112 C.P. 90

 C.P. = 90 M.P. 112

 C.P. = 45 M.P. 56

C.P. : M.P. = 45 : 56

1. A manufacturer marked an article at ₹ 50 and sold it allowing 20% discount. If his profit was 25%, then the cost price of the article was
1. ₹ 40
2. ₹ 35
3. ₹ 32
4. ₹ 30

1. Marked price = 50
S.P. after 20% discount = 80% of 50 = ₹ 40
If the CP of article be y, then

 125 × y = 40 100

 ⇒  y = 40 × 100 = ₹ 32 125

Second method :
Here, M.P. = ₹ 50, C.P. = ?, r = 25%, D = 20%
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: C

Marked price = 50
S.P. after 20% discount = 80% of 50 = ₹ 40
If the CP of article be y, then

 125 × y = 40 100

 ⇒  y = 40 × 100 = ₹ 32 125

Second method :
Here, M.P. = ₹ 50, C.P. = ?, r = 25%, D = 20%
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

 50 = 100 + 25 C.P. 100 − 20

 C.P. = 50 × 80 = ₹ 32 125

1. The marked price of an electric iron is ₹ 300. The shopkeeper allows a discount of 12% and still gains 10%. If no discount is allowed, his gain per cent would have been :
1. 20%
2. 25%
3. 27%
4. 30%

1. Here , The marked price of an electric iron = ₹ 300
Discount = 12%
According to question ,
SP of electric iron = 88% of 300

 SP of electric iron = ₹ 300 × 88 = ₹ 264 100

Profit = 10%
 ∴  CP of electric iron = 100 × 264 = ₹ 240 110

After no discount,
Gain = 300 – 240 = ₹ 60
 Gain percent = 60 × 100 = 25% 240

Second Method :
Here, M.P. = ₹ 300, r = 10%, D = 12%.
With the help of given formula ,
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: B

Here , The marked price of an electric iron = ₹ 300
Discount = 12%
According to question ,
SP of electric iron = 88% of 300

 SP of electric iron = ₹ 300 × 88 = ₹ 264 100

Profit = 10%
 ∴  CP of electric iron = 100 × 264 = ₹ 240 110

After no discount,
Gain = 300 – 240 = ₹ 60
 Gain percent = 60 × 100 = 25% 240

Second Method :
Here, M.P. = ₹ 300, r = 10%, D = 12%.
With the help of given formula ,
 M.P. = 100 + r C.P. 100 − D

 300 = 100 + 10 C.P. 100 − 12

 C.P. = 300 × 88 110

 Gain % (without discount) = 300 − 240 × 100 = 25% 240