## Discount

#### Discount

1. The marked price of an article is ₹ 500. A shopkeeper gives a discount of 5% and still makes a profit of 25%. The cost price of the article is.
1. ₹ 384
2. ₹ 380
3. ₹ 300
4. ₹ 376

1. Let Cost price of the article = ₹ p

 ∴  p × 125 = 500 × 95 100 100

2nd method to solve this question.
Here, R = 25%, D = 5%,
M.P. = ₹ 500, C.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: B

Let Cost price of the article = ₹ p

 ∴  p × 125 = 500 × 95 100 100

 ⇒  p = 500 × 95 = ₹ 380 125

2nd method to solve this question.
Here, R = 25%, D = 5%,
M.P. = ₹ 500, C.P. = ?
 M.P. = 100 + r C.P. 100 − D

 500 = 100 + 25 C.P. 100 − 5

 C.P.= 500 × 95 = ₹ 380 125

1. Anand marks up the price of an article by 50 % and then allows a discount of 20 % and sells it to Balaji. Balaji sells it for ₹ 20 more than what he purchased for, this S.P is 30 % more than the original C.P of the article. Then Balaji’s profit % is
1. 7.5%
2. 6.66%
3. 8.33%
4. 9%

1. Let us assume the cost price = ₹ p
For Anand,

 Marked price = ₹ 3 p 2

 Selling price = 3p × 80 2 100

For Balaji,
 Cost price = ₹ 6p 5

 Selling price = ₹ 6p + 20 5

 ∴ 6p + 20 = p × 130 5 100

##### Correct Option: C

Let us assume the cost price = ₹ p
For Anand,

 Marked price = ₹ 3 p 2

 Selling price = 3p × 80 2 100

 = ₹ 6p 5

For Balaji,
 Cost price = ₹ 6p 5

 Selling price = ₹ 6p + 20 5

 ∴ 6p + 20 = p × 130 5 100

 ⇒ 13p − 6p = 20 10 5

 ⇒ 13p − 12p = 20 10

 ⇒ p = 20 10

⇒  p = ₹ 200
 ∴  Required gain percent = 20 ×100 6p 5

 ⇒  Required gain percent = 20 × 5 × 100 6 × p

 ⇒  Required gain percent = 20 × 5 × 100 = 25 = 8.33% 6 × 200 3

∴ Required gain percent is 8.33% .

1. A merchant purchases a wrist watch for ₹ 450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Find the list price of the watch.
1. ₹ 480
2. ₹ 450
3. ₹ 600
4. ₹ 540

1. Let marked price of the wrist watch be p.

 ∴ 90p = 450 × 120 100 100

⇒  90p = 450 × 120
 ∴  p = 450 × 120 = ₹ 600 90

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

 20 = r × (100 − 10) − 10 100

 20 = 9r − 10 10

##### Correct Option: C

Let marked price of the wrist watch be p

 ∴ 90p = 450 × 120 100 100

⇒  90p = 450 × 120
 ∴  p = 450 × 120 = ₹ 600 90

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

 20 = r × (100 − 10) − 10 100

 20 = 9r − 10 10

 30 = 9r 10

 r = 300 % 9

 ∴  List price = 450 + 450 × 300 % 9

 List price = 450 + 450 × 300 900

Required List price = 450 + 150 = ₹ 600

1. A merchant allows a discount of 10% on marked price for the cash payment. To make a profit of 17%, he must mark his goods higher than their cost price by
1. 33%
2. 40%
3. 27%
4. 30%

1. C.P. of article = ₹ 100
Let marked price of article p.

 ∴  p × 90 = 117 100

2nd method to solve this question.
Here, r1 = 10%, Gain % = 17%, r = ?
 Gain % = r ×(100 − r1) − r1 100

##### Correct Option: D

C.P. of article = ₹ 100
Let marked price of article p.

 ∴  p × 90 = 117 100

 ⇒  p = 117 × 100 90

= ₹ 130 or 30% above the cost price.
2nd method to solve this question.
Here, r1 = 10%, Gain % = 17%, r = ?
 Gain % = r ×(100 − r1) − r1 100

 17 = r × (100 − 10) − 10 100

 27 = r × 90 100

r = 30%

1. In a shop, shirts are usually sold at 40% above the cost price. During a sale, the shopkeeper offers a discount of 10% off the usual selling price. If he manages to sell 72 shirts for ₹ 13,608, then his cost price per shirt, (in ₹) is
1. 210
2. 150
3. 149
4. 125

1. Let the CP of each shirt be
₹ 100, then SP = ₹ 140.

 ∴  New SP = 140 × 90 = ₹ 126 100

∴  When S.P. is ₹ 126
C.P. = ₹ 100
 ∴  When S.P. is ₹ 13680 , 72

##### Correct Option: B

Let the CP of each shirt be
₹ 100, then SP = ₹ 140.

 ∴  New SP = 140 × 90 = ₹ 126 100

∴  When S.P. is ₹ 126
C.P. = ₹ 100
 ∴  When S.P. is ₹ 13680 , 72

 then C.P. = 100 × 13680 = ₹ 150 126 72