## Discount

#### Discount

1. By giving a discount of 10% on the marked price of ₹ 1100 of a cycle, a dealer gains 10%. The cost price of the cycle is :
1. ₹ 1100
2. ₹ 900
3. ₹ 1089
4. ₹ 891

1. Given that , discount = 10% and marked price of cycle = ₹ 1100
Selling Price = ₹ (1100 – 10% of 1100) = ₹ (1100 – 110) = 990
Let the cost price = y
According to question ,
∴  y + 10% of y = 990

 ⇒ 11y = 990 10

 ⇒  y = 990 × 10 = ₹ 900 11

Second method to solve this question :
Here, r = 10% , D = 10% , M.P. = ₹ 1100 , C.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: B

Given that , discount = 10% and marked price of cycle = ₹ 1100
Selling Price = ₹ (1100 – 10% of 1100) = ₹ (1100 – 110) = 990
Let the cost price = y
According to question ,
∴  y + 10% of y = 990

 ⇒ 11y = 990 10

 ⇒  y = 990 × 10 = ₹ 900 11

Second method to solve this question :
Here, r = 10% , D = 10% , M.P. = ₹ 1100 , C.P. = ?
 M.P. = 100 + r C.P. 100 − D

 1100 = 100 + 10 C.P. 100 − 10

 C.P. = 1100 × 90 = ₹ 900 110

1. A shopkeeper earns a profit of 10% after allowing a discount of 20% on the marked price. The cost price of the article whose marked price is ₹ 880, is
1. ₹ 704
2. ₹ 640
3. ₹ 774
4. ₹ 680

1. Given Here , marked price = ₹ 880
SP of article = (100 – 20)% of 880 = 80% of 880
Let CP be y
Again, 110% of y = 704

 y = 704 × 100 = ₹ 640 110

∴  Original cost = ₹ 640
We can find required answer with the help of given formula :
Here, r = 10%, D = 20%, M.P. = ₹ 880, C.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: B

Given Here , marked price = ₹ 880
SP of article = (100 – 20)% of 880 = 80% of 880
Let CP be y
Again, 110% of y = 704

 y = 704 × 100 = ₹ 640 110

∴  Original cost = ₹ 640
We can find required answer with the help of given formula :
Here, r = 10%, D = 20%, M.P. = ₹ 880, C.P. = ?
 M.P. = 100 + r C.P. 100 − D

 880 = 100 + 10 C.P. 100 − 20

 880 = 110 C.P. 80

 C.P. = 880 × 80 110

C.P. = ₹ 640

1.  The marked price of an article is ₹ 200. A discount of 12 1 % is allowed on the marked price 2
and a profit of 25% is made. The cost price of the article is :
1. ₹ 200
2. ₹ 175
3. ₹ 120
4. ₹ 140

1. Given that , marked price of an article = ₹ 200

 Discount = 12 1 % = 25 % 2 2

After discount , S.P. = ₹ 200 × 87.5 = ₹ 175
Gain % = 25%
 Required C.P. = ₹ 100 × 175 = ₹ 140 125

Using the given formula :
Here, r = 25% , D = 12.5% , M.P. = ₹ 200 , C.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: D

Given that , marked price of an article = ₹ 200

 Discount = 12 1 % = 25 % 2 2

After discount , S.P. = ₹ 200 × 87.5 = ₹ 175
Gain % = 25%
 Required C.P. = ₹ 100 × 175 = ₹ 140 125

Using the given formula :
Here, r = 25% , D = 12.5% , M.P. = ₹ 200 , C.P. = ?
 M.P. = 100 + r C.P. 100 − D

 200 = 100 + 25 C.P. 100 − 12.5

 C.P. = 200 × 87.5 125

C.P. = ₹ 140

1. A dealer offers a discount of 10% on the marked price of an article and still makes a profit of 20%. If its marked price is ₹ 800, then the cost price of the article is :
1. ₹ 900
2. ₹ 800
3. ₹ 700
4. ₹ 600

1. Here , marked price = ₹ 800
On discount of 10% ,

 S.P. of that article = 800 × 90 = ₹ 720 100

He still makes 20% profit
 ∴  C.P. of the article = 720 × 100 = ₹ 600 120

Second method to solve this question :
Here, r = 20% , D = 10% , M.P. = ₹ 800 , C.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: D

Here , marked price = ₹ 800
On discount of 10% ,

 S.P. of that article = 800 × 90 = ₹ 720 100

He still makes 20% profit
 ∴  C.P. of the article = 720 × 100 = ₹ 600 120

Second method to solve this question :
Here, r = 20% , D = 10% , M.P. = ₹ 800 , C.P. = ?
 M.P. = 100 + r C.P. 100 − D

 800 = 100 + 20 C.P. 100 − 10

 C.P. = 800 × 90 120

C.P. = ₹ 600

1. A shopkeeper marks his goods 50% more than the cost price and allows a discount of 25%. His profit or loss percentage is :
1. 37.5%
2. 25.5%
3. 12.5%
4. 25%

1. Let C.P. of article be Rs. 100.
∴  Marked price = Rs. 150
discount = 25%

 S.P. of article = Rs. 150 × 75 = Rs. 112.5 100

∴  Profit = S.P. of article - C.P. of article = Rs. (112.5 – 100) = Rs. 12.5

##### Correct Option: C

Let C.P. of article be Rs. 100.
∴  Marked price = Rs. 150
discount = 25%

 S.P. of article = Rs. 150 × 75 = Rs. 112.5 100

∴  Profit = S.P. of article - C.P. of article = Rs. (112.5 – 100) = Rs. 12.5
 ∴ Profit percent = Profit × 100 C.P.

 Profit percent = 12.5 × 100 = 12.5% 100