## Discount

#### Discount

1. 20% profit is made when a discount of 20% is given on the marked price. When the discount is 30% profit will be
1. 4%
2. 5%
3. 6%
4. 7.5%

1. Let the marked price of article be Rs. M and its C.P. be Rs. 100.
According to the question,

 M × 80 = 100 × 120 100 100

 ⇒  M = 120 × 100 = Rs. 150 90

##### Correct Option: B

Let the marked price of article be Rs. M and its C.P. be Rs. 100.
According to the question,

 M × 80 = 100 × 120 100 100

 ⇒  M = 120 × 100 = Rs. 150 90

 S.P. after a discount of 30% = 150 × 70 100

Selling Price = Rs. 105 i.e. gain = 5%

1. A shopkeeper allows a discount of 10% on the marked price of a camera. Marked price of the camera, which costs him ₹ 600, to make a profit of 20% should be
1. 700
2. 750
3. 650
4. 800

1. Let the marked price of the camera be Rs. m.
According to the question,

 m × 90 = 600 × 120 100 100

2nd method to solve this question.
Here, r = 20%
D = 10%
C.P. = Rs. 600
M.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: D

Let the marked price of the camera be Rs. m.
According to the question,

 m × 90 = 600 × 120 100 100

⇒  m × 90 = 600 × 120
 ⇒  m = 600 × 120 = Rs. 800 90

2nd method to solve this question.
Here, r = 20%
D = 10%
C.P. = Rs. 600
M.P. = ?
 M.P. = 100 + r C.P. 100 − D

 M.P. = 100 + 20 600 100 − 10

 M.P. = 120 × 600 = 800 90

1. A tradesman marks his goods at 20 % above the cost price. He allows his customers a discount of 8% on the marked price. Then his profit % is
1. 10.4%
2. 11%
3. 12.2%
4. 9.7%

1. Let the C.P. of article be Rs. 100,
According to the questions
Marked price of article = Rs. 120
After a discount of 8%,

 S.P. = 120 × 92 100

= Rs. 110.4 Gain
= Rs. (110.4 – 100) = Rs. 10.4
∴  Gain % = 10.4%
2nd method to solve this question.
Here, r = 20%, r1 = 8%
 ⇒ Gain % = r × (100 − r1) − r1 100

##### Correct Option: A

Let the C.P. of article be Rs. 100,
According to the questions
Marked price of article = Rs. 120
After a discount of 8%,

 S.P. = 120 × 92 100

= Rs. 110.4 Gain
= Rs. (110.4 – 100) = Rs. 10.4
∴  Gain % = 10.4%
2nd method to solve this question.
Here, r = 20%, r1 = 8%
 ⇒ Gain % = r × (100 − r1) − r1 100

 Gain % = 20 × (100 − 8) − 8 100

 Gain % = 20 × 92 − 8 100

Required Gain % = 18.4 – 8 = 10.4%

1. If a person marks a product 25% above the cost price but allows 10% discount, then the percentage of profit is
1. 35 %
2. 15 %
3. 17.5 %
4. 12.5 %

1. As we know the formula for profit %

 Profit percent = q + r + qr % 100

2nd method to solve this question.
Here = r = 25%, r1 = 10%
 ⇒ Gain % = r ×(100 − r1) − r1 100

##### Correct Option: D

As we know the formula for profit %

 Profit percent = q + r + qr % 100

 = 25 − 10 − 25 × 10 % 100

= (15 – 2.5)% = 12.5 %
2nd method to solve this question.
Here = r = 25%, r1 = 10%
 ⇒ Gain % = r ×(100 − r1) − r1 100

 Gain % = 25 × (100 − 10) − 10 100

 Gain % = 25 × 90 − 10 100

Required Gain % = 22.5 – 10 = 12.5%

1. A dealer of scientific instruments allows 20% discount on the marked price of the instruments and still makes a profit of 25%. If his gain over the sale of an instrument is ₹ 150, find the marked price of the instrument.
1. ₹ 938.50
2. ₹ 940
3. ₹ 938
4. ₹ 937.50

1. Let Marked price of instrument = Rs. p

 ∴  Its S.P. = Rs. 80p 100

 S.P. = Rs. 4p 5

 ∴  C.P.= Rs. 4p − 150 5

 ∴ 4p = 4p − 150 × 125 5 5 100

 ⇒ 4p = 4p − 150 × 5 5 5 4

 ⇒ 4p × 4 = 4p − 150 5 5 5

 ⇒ 4p − 16p = 150 5 25

##### Correct Option: D

Let Marked price of instrument = Rs. p

 ∴  Its S.P. = Rs. 80p 100

 S.P. = Rs. 4p 5

 ∴  C.P.= Rs. 4p − 150 5

 ∴ 4p = 4p − 150 × 125 5 5 100

 ⇒ 4p = 4p − 150 × 5 5 5 4

 ⇒ 4p × 4 = 4p − 150 5 5 5

 ⇒ 4p − 16p = 150 5 25

 ⇒ 20p − 16x = 150 25

 ⇒ 4p = 150 ⇒ 4p = 150 × 25 25

 ⇒  p = 150 × 25 = Rs. 937.5 4