Discount

Discount

1. After allowing a discount of 12% on the marked price, a shopkeeper still gains 21%. The marked price is above the cost price by
1. 25%
2. 30%
3. 37.5%
4. 42.5%

1. Given that , discount = 12% and gains = 21%
C.P. of article = ₹ 100
Marked price be y .

 ∴ y × 88 = 121 100

 ⇒  y = 121 × 100 = ₹ 137.5 88

∴ 137.5 - 100 = ₹ 37.5 i.e. 37.5% above C.P.
Second method to solve this question :
Here, r = 12% , R = 21%
With the help of given formula ,
 Required percentage = r + R × 100 % 100 − r

Correct Option: C

Given that , discount = 12% and gains = 21%
C.P. of article = ₹ 100
Marked price be y .

 ∴ y × 88 = 121 100

 ⇒  y = 121 × 100 = ₹ 137.5 88

∴ 137.5 - 100 = ₹ 37.5 i.e. 37.5% above C.P.
Second method to solve this question :
Here, r = 12% , R = 21%
With the help of given formula ,
 Required percentage = r + R × 100 % 100 − r

 Required percentage = 12 + 21 × 100% 100 − 12

 Required percentage = 33 × 100% 88

 = 3 × 100 8

 Required percentage = 300 % = 37.5% 8

1. How much percent above the cost price should a shopkeeper mark his goods so as to earn a profit of 32% after allowing a discount of 12% on the marked price ?
1. 50%
2. 40%
3. 60%
4. 45%

1. Given in question , Profit = 32% and discount = 12%
Let the C.P. be 100 and the marked price be y.

 ∴  y × 88 = 132 100

 ⇒  x = 132 × 100 88

= 150 i.e., more by 50%
Second method to solve this question :
Here, r = 12% , R = 32%
 Required percentage = r + R × 100 % 100 − r

Correct Option: A

Given in question , Profit = 32% and discount = 12%
Let the C.P. be 100 and the marked price be y.

 ∴  y × 88 = 132 100

 ⇒  x = 132 × 100 88

= 150 i.e., more by 50%
Second method to solve this question :
Here, r = 12% , R = 32%
 Required percentage = r + R × 100 % 100 − r

 Required percentage = 12 + 32 × 100% 100 − 12

 Required percentage = 44 × 100 = 50% 88

1. A tradesman marks his goods at such a price that after allowing a discount of 15%, he makes a profit of 20%. What is the marked price of an article whose cost price is ₹ 170 ?
1. ₹ 240
2. ₹ 260
3. ₹ 220
4. ₹ 200

1. Here , Cost price = ₹ 170 , discount = 15% , profit = 20%
If the marked price be y, then

 y × 85 = 170 × 120 100 100

 ⇒  y = 170 × 120 = ₹ 240 85

Second method :
Given Here, D = 15% , r = 20% , C.P. = ₹ 170
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

Correct Option: A

Here , Cost price = ₹ 170 , discount = 15% , profit = 20%
If the marked price be y, then

 y × 85 = 170 × 120 100 100

 ⇒  y = 170 × 120 = ₹ 240 85

Second method :
Given Here, D = 15% , r = 20% , C.P. = ₹ 170
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

 M.P. = 100 + 20 170 100 − 15

 M.P. = 120 170 85

 M.P. = 120 × 170 = ₹ 240 85

1.  A trader allows a trade discount of 20% and a cash discount of 6 1 % on the 4

marked price of the goods and gets a net gain of 20% of the cost. By how much above the cost should the goods be marked for the sale ?
1. 40%
2. 50%
3. 60%
4. 70%

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

 Single equivalent discount for a% and b% = a + b - a × b % 100

Here , a = 20% , b = ( 25 /4 )%
 Single equivalent discount = 20 + 25 − 20 × 25 % = 25% 4 400

Correct Option: C

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

 Single equivalent discount for a% and b% = a + b - a × b % 100

Here , a = 20% , b = ( 25 /4 )%
 Single equivalent discount = 20 + 25 − 20 × 25 % = 25% 4 400

On 25% discount ,
 ∴  y × 75 = 120 100

 ⇒  y = 120 × 100 = ₹ 160 75

Marked price = ₹ 160
⇒  160 – 100 = 60
 Required percent = 60 × 100 = 60% 100

1. An article of cost price ₹ 8,000 is marked at ₹ 11,200. After allowing a discount of x% a profit of 12% is made. The value of x is
1. 21%
2. 20%
3. 22%
4. 23%

1. Here , cost price of article = ₹ 8,000 and marked price = ₹ 11,200

 S.P. for a profit of 12% = 8000 × 112 = ₹ 8960 100

∴  Discount = marked price - S.P.
∴  Discount = 11200 – 8960 =₹ 2240
If the discount percent be x, then
 11200 × x = 2240 100

 x = 2240 × 100 = 20% 11200

Second method :
Here, M.P. = ₹ 11200 , C.P. = ₹ 8000 , r = 12% , D = x%
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

Correct Option: B

Here , cost price of article = ₹ 8,000 and marked price = ₹ 11,200

 S.P. for a profit of 12% = 8000 × 112 = ₹ 8960 100

∴  Discount = marked price - S.P.
∴  Discount = 11200 – 8960 =₹ 2240
If the discount percent be x, then
 11200 × x = 2240 100

 x = 2240 × 100 = 20% 11200

Second method :
Here, M.P. = ₹ 11200 , C.P. = ₹ 8000 , r = 12% , D = x%
Using the given formula ,
 M.P. = 100 + r C.P. 100 − D

 11200 = 100 + 12 8000 100 − x

 = 11200 = 112 8000 100 − x

⇒ 100 – x = 80
⇒ x = 20%