## Discount

#### Discount

1. A shopkeeper marks his goods 40% above the cost price. He allows a discount of 5% for cash payment to his customers. He receives ₹ 1064 after paying the discount. His profit is
1. ₹ 264
2. ₹ 164
3. ₹ 200
4. ₹ 800

1. Given that , discount = 5%
Suppose Cost price of article = ₹ y

 ∴  y × 140 × 95 = 1064 100 100

##### Correct Option: D

Given that , discount = 5%
Suppose Cost price of article = ₹ y

 ∴  y × 140 × 95 = 1064 100 100

 ⇒  y = 1064 × 100 × 100 = ₹ 800 140 × 95

Hence , Cost price of article is ₹ 800 .

1. A shopkeeper marks his goods 20% above his cost price and gives 15% discount on the marked price. His gain percent is
1. 5%
2. 4%
3. 2%
4. 1%

1. If the C.P. of goods be ₹ 100, then
Marked price = ₹ 120
discount = 15%

 ∴  S.P. = 120 × 85 = ₹ 102 100

Profit = S.P. - C.P. = 102 - 100 = ₹ 2
 Hence, Required percent = 2 × 100 = 2% 100

Second method :
Here, r = 20%, r1 = 15%
Using the given formula ,
 Gain % = r × (100 − r1) − r1 100

##### Correct Option: C

If the C.P. of goods be ₹ 100, then
Marked price = ₹ 120
discount = 15%

 ∴  S.P. = 120 × 85 = ₹ 102 100

Profit = S.P. - C.P. = 102 - 100 = ₹ 2
 Hence, Required percent = 2 × 100 = 2% 100

Second method :
Here, r = 20%, r1 = 15%
Using the given formula ,
 Gain % = r × (100 − r1) − r1 100

 Gain % = 20 × (100 − 15) − 15 100

 = 20 × 85 − 15 100

Gain % = 17 – 15 = 2%

1. How much percent more than the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gains 20% ?
1. 70%
2. 50%
3. 60%
4. 55%

1. Given that , discount = 25% and gains = 20%
Let C.P.of article = 100
If the marked price of article be y, then

 y × 75 = 120 100

 ⇒  y = 120 × 100 = 160 75

⇒ 160 - 100 = ₹ 60 i.e. 60% above the cost price .
Second method to solve this question :
Here . r = 25%, R = 20%
 Required percentage = r + R × 100 % 100 − r

##### Correct Option: C

Given that , discount = 25% and gains = 20%
Let C.P.of article = 100
If the marked price of article be y, then

 y × 75 = 120 100

 ⇒  y = 120 × 100 = 160 75

⇒ 160 - 100 = ₹ 60 i.e. 60% above the cost price .
Second method to solve this question :
Here . r = 25%, R = 20%
 Required percentage = r + R × 100 % 100 − r

 Required percentage = 25 + 20 × 100% 100 − 25

 Required percentage = 45 × 100 = 60% 75

1. A grinder was marked at ₹ 3,600. After given a discount of 10% the dealer made a profit of 8%. Calculate the cost price.
1. ₹ 3,000
2. ₹ 3,312
3. ₹ 3,240
4. ₹ 2,960

1. Here , marked price = ₹ 3,600 , discount = 10% , profit = 8%
If the C.P. of grinder be y, then

 y × 108 = 3600 × 90 = 3240 100 100

 ⇒  y = 3240 × 100 = ₹ 3000 108

Second method :
Given that , M.P. = ₹ 3600, D = 10%, r = 8%, C.P. = ?
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: A

Here , marked price = ₹ 3,600 , discount = 10% , profit = 8%
If the C.P. of grinder be y, then

 y × 108 = 3600 × 90 = 3240 100 100

 ⇒  y = 3240 × 100 = ₹ 3000 108

Second method :
Given that , M.P. = ₹ 3600, D = 10%, r = 8%, C.P. = ?
 M.P. = 100 + r C.P. 100 − D

 3600 = 100 + 8 C.P. 100 − 10

 C.P. = 3600 × 90 108

 C.P. = 3600 × 10 = ₹ 3000 12

1. A profit of 10% is made after giving a discount of 5% on a T. V. If the marked price of the TV is ₹ 2640.00, the cost price of the TV was :
1. ₹ 2280
2. ₹ 2296
3. ₹ 2380
4. ₹ 2396

1. Here , profit = 10% and discount = 5%
Let the C.P. of TV be y, then

 y × 110 = 2640 × 95 100 100

 ⇒  y = 2640 × 95 = ₹ 2280 110

Second method :
Here, r = 10% , D = 5% , M.P. = ₹ 2640 , C.P. = ?
We can find required answer with the help of given formula ,
 M.P. = 100 + r C.P. 100 − D

##### Correct Option: A

Here , profit = 10% and discount = 5%
Let the C.P. of TV be y, then

 y × 110 = 2640 × 95 100 100

 ⇒  y = 2640 × 95 = ₹ 2280 110

Second method :
Here, r = 10% , D = 5% , M.P. = ₹ 2640 , C.P. = ?
We can find required answer with the help of given formula ,
 M.P. = 100 + r C.P. 100 − D

 2640 = 100 + 10 C.P. 100 − 5

 C.P. = 2640 × 95 110

C.P. = 24 × 95 = ₹ 2280