## Discount

#### Discount

1. A dealer allows his customers a discount of 25% and still gains 25%. If an article costs Rs. 1,440 to the dealer; then its marked price is
1. Rs. 1,850
2. Rs. 2,400
3. Rs. 2,560
4. Rs. 1,500

1. Let the marked price of article be Rs. x
According to the question,

 x × 75 = 1440 × 125 100 100

 ⇒  x = 1440 × 125 = Rs. 2400 75

Second method :
Here, D = 25%, r = 25%, C.P. = Rs. 1440, M.P. = ?
 M.P. = 100 + r C.P. 100 − D

 M.P. = 100 + 25 1440 100 − 25

 M.P. = 125 × 1440 = Rs. 2400 75

##### Correct Option: B

Let the marked price of article be Rs. x
According to the question,

 x × 75 = 1440 × 125 100 100

 ⇒  x = 1440 × 125 = Rs. 2400 75

Second method :
Here, D = 25%, r = 25%, C.P. = Rs. 1440, M.P. = ?
 M.P. = 100 + r C.P. 100 − D

 M.P. = 100 + 25 1440 100 − 25

 M.P. = 125 × 1440 = Rs. 2400 75

1. The listed price of a shirt is ₹ 270 and it is available at ₹ 237.60. The rate of discount is
1. 10%
2. 12%
3. 15%
4. 20%

1. Discount = 270 – 237.60 = Rs. 32.4
If the rate of discount be x%, then

 270 × x = 32.4 100

 ⇒  x = 32.4 × 100 = 12% 270

Second method :
Here, S.P. = Rs. 237.60,
M.P. = Rs. 270
 Discount % = M.P. − S.P. × 100% M.P.

 = 270 − 237.60 × 100% 270

 = 32.40 × 100 % = 12% 270

##### Correct Option: B

Discount = 270 – 237.60 = Rs. 32.4
If the rate of discount be x%, then

 270 × x = 32.4 100

 ⇒  x = 32.4 × 100 = 12% 270

Second method :
Here, S.P. = Rs. 237.60,
M.P. = Rs. 270
 Discount % = M.P. − S.P. × 100% M.P.

 = 270 − 237.60 × 100% 270

 = 32.40 × 100 % = 12% 270

1. The marked price of an item is twice the cost price. For a gain of 15%, the discount should be
1. 7.5%
2. 20.5%
3. 32.5%
4. 42.5%

1. C.P. of item = 100 (let)
∴  Marked price of item = ₹ 200
S.P. for a gain of 15% = ₹ 115
∴  Discount = 200 – 115 = ₹ 85
If discount percent be x%, then

 200 × x = 85 100

 ⇒ 2x = 85 ⇒ x = 85 = 42.5% 2

Second method :
Let, C.P. = ₹ x,
M.P. = ₹ 2x, r = 15%
 M.P. = 100 + r C.P. 100 − D

 2x = 100 + 15 x 100 − D

200 – 2D = 115
2D = 85
D = 42.5%

##### Correct Option: D

C.P. of item = 100 (let)
∴  Marked price of item = ₹ 200
S.P. for a gain of 15% = ₹ 115
∴  Discount = 200 – 115 = ₹ 85
If discount percent be x%, then

 200 × x = 85 100

 ⇒ 2x = 85 ⇒ x = 85 = 42.5% 2

Second method :
Let, C.P. = ₹ x,
M.P. = ₹ 2x, r = 15%
 M.P. = 100 + r C.P. 100 − D

 2x = 100 + 15 x 100 − D

200 – 2D = 115
2D = 85
D = 42.5%

1. A table with marked price ₹ 1200 was sold to a customer for ₹ 1100. Find the rate of discount allowed on the table.
1. 9%
2.  8 1 % 3
3.  9 1 % 3
4. 10%

1. Rate of discount = x%

 ∴  1200 × x = 1200 − 1100 100

⇒  12x = 100
 ⇒ x = 100 = 25 = 8 1 % 12 3 3

Second method :
Here, M.P. = ₹ 1200,
S.P. = ₹ 1100
 Discount % = M.P. − S.P. × 100 M.P.

 = 1200 − 1100 × 100 1200

 = 100 × 100 = 8 1 % 1200 3

##### Correct Option: B

Rate of discount = x%

 ∴  1200 × x = 1200 − 1100 100

⇒  12x = 100
 ⇒ x = 100 = 25 = 8 1 % 12 3 3

Second method :
Here, M.P. = ₹ 1200,
S.P. = ₹ 1100
 Discount % = M.P. − S.P. × 100 M.P.

 = 1200 − 1100 × 100 1200

 = 100 × 100 = 8 1 % 1200 3

1. A machine is marked at ₹ 6,800 and available at a discount of 10%. The shopkeeper gives another off season discount to the buyer and sells the machine for ₹ 5,202. Find the off season discount.
1. 10%
2. 12%
3. 15%
4. 18%

1.  Price after discount of 10% = 6800 × 90 = ₹ 6120 100

If the seasonal discount be x%, then
 6120 × x = 6120 – 5202 = 918 100

 ⇒  x = 918 × 100 = 15% 6120

##### Correct Option: C

 Price after discount of 10% = 6800 × 90 = ₹ 6120 100

If the seasonal discount be x%, then
 6120 × x = 6120 – 5202 = 918 100

 ⇒  x = 918 × 100 = 15% 6120