## Discount

#### Discount

1. The marked price of an article is 10 % higher than the cost price. A discount of 10 % is given on the marked price. In this kind of sale, the seller bears.
1. no loss, no gain
2. a loss of 5%
3. a gain of 1%
4. a loss of 1%

1. Let C.P. of article = ₹ 100
Marked price = ₹ 110

 S.P. = 110 × 90 = ₹ 99 100

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

##### Correct Option: D

Let C.P. of article = ₹ 100
Marked price = ₹ 110

 S.P. = 110 × 90 = ₹ 99 100

Loss = 100 – 99 = ₹ 1 = 1%
2nd method to solve this question.
Here, r = 10%, r1 = 10%
 Gain or Loss %= r ×(100 − r1) − r1 100

 Gain or Loss % = 10 × (100 − 10) − 10 100

Gain or Loss % = 9 – 10 = –1 (–ve sign shows loss)
⇒  Loss = 1%

1. Charging 30 % above its production cost a radio maker puts a label of ₹ 286 on a radio as its price. But at the time of selling it, he allows 10 % discount on the labelled price. What will his gain be ?
1. ₹ 257 .40
2. ₹ 254. 40
3. ₹ 198
4. ₹ 37. 40

1. Let Production cost of radio= ₹ p

 ∴ p × 130 = 286 100

 ⇒  p = 286 × 100 = ₹ 220 130

∴  Selling price = 90% of 286

##### Correct Option: D

Let Production cost of radio= ₹ p

 ∴ p × 130 = 286 100

 ⇒  p = 286 × 100 = ₹ 220 130

∴  Selling price = 90% of 286
 ∴  Selling price = 286 × 90 = ₹ 257.40 100

Required Profit = ₹ (257.40 – 220) = ₹ 37.40

1. A businessman allows a discount of 10 % on the marked price. What percent above the cost price must he mark his goods to make a profit of 17 percent ?
1. 27 %
2. 18 %
3. 30 %
4. 20 %

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

 ∴  p × 90 = 117 100

2nd method to solve this question.
Let, C.P. = ₹ 100, r = 17%, D = 10%, M.P. = ?
 M.P. = 100 + r C.P. 100 − r

##### Correct Option: C

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

 ∴  p × 90 = 117 100

 ⇒  p = 117 × 100 = ₹ 130 90

i.e. 30% above the cost price.
2nd method to solve this question.
Let, C.P. = ₹ 100, r = 17%, D = 10%, M.P. = ?
 M.P. = 100 + r C.P. 100 − r

 M.P. = 100 + 17 100 100 − 10

 M.P. = 117 × 100 90

⇒  30% above cost price.

1. A shopkeeper allows a discount of 10% on the marked price of an item but charges a sales tax of 8% on the discounted price. If the customer pays ₹ 3,402 as the price including the sales tax, then the marked price is
1. ₹ 3,400
2. ₹ 3,500
3. ₹ 3,600
4. ₹ 3,800

1. Let Marked price of article = ₹ p

 ∴  S.P. of article = ₹ p × 90 × 108 100 100

##### Correct Option: B

Let Marked price of article = ₹ p

 ∴  S.P. of article = ₹ p × 90 × 108 100 100

 ∴  p × 90 × 108 = 3402 9 9

 ⇒  p = 3402 × 100 × 100 90 × 108

Hence Marked price of article = ₹ 3500

1. If the discount is equal to one fifth of the marked price and the loss is half the discount, then the percentage of loss is
1.  10 1 % 9
2.  11 1 % 9
3.  12 1 % 9
4.  13 1 % 9

1. Let Marked price = ₹ p

 Discount = ₹ p 5

 S.P. = p − p = ₹ 4p 5 5

 Loss = ₹ p 10

 ∴  C.P. = 4p + p 5 10

 = 8p + p = ₹ 9p 10 10

##### Correct Option: B

Let Marked price = ₹ p

 Discount = ₹ p 5

 S.P. = p − p = ₹ 4p 5 5

 Loss = ₹ p 10

 ∴  C.P. = 4p + p 5 10

 = 8p + p = ₹ 9p 10 10

 ∴  Loss percent = p/10 ×100 9p/10

 Hence ,Loss percent = 100 = 11 1 % 9 9