Discount
- 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% ?
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Given that , discount = 25% and gains = 20%
Let C.P.of article = 100
If the marked price of article be y, theny × 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, theny × 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
- After allowing a discount of 16%, there was still a gain of 5%. Then the percentage of marked price over the cost price is
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Let the C.P. of article be ₹ 100 and its marked price be y.
Discount = 16% and gain = 5%∴ y × 84 = 105 100 ⇒ y = 105 × 100 = 125 84
Difference = 125 - 100 = 25
∵ C.P. of article = ₹ 100
∴ Required percentage = 25%
Second method to solve this question :
Here, r = 5% , D = 16%
Using the given formula ,M.P. = 100 + r C.P. 100 − D
Correct Option: D
Let the C.P. of article be ₹ 100 and its marked price be y.
Discount = 16% and gain = 5%∴ y × 84 = 105 100 ⇒ y = 105 × 100 = 125 84
Difference = 125 - 100 = 25
∵ C.P. of article = ₹ 100
∴ Required percentage = 25%
Second method to solve this question :
Here, r = 5% , D = 16%
Using the given formula ,M.P. = 100 + r C.P. 100 − D M.P. = 100 + 5 = 105 C.P. 100 − 16 84 Required Percentage = 105 − 84 × 100 = 25% 84
- The marked price of a radio is ₹ 4,800. The shopkeeper allows a discount of 10% and gains 8%. If no discount is allowed, his gain per cent will be
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Here , marked price of a radio = ₹ 4,800 , discount = 10% and gains = 8%
Let CP of radio be Rs. y.
According to the question,108y = 4800 × 90 = 4320 100 100 ⇒ y = 4320 × 100 = ₹ 4000 108
Gain = 4800 - 4000 = ₹ 800
If no discount is allowed,thenGain percent = 800 × 100 = 20% 4000
Second method :
Given Here , M.P. = ₹ 4800, D = 10%, r = 8%
With the help of given formula ,M.P. = 100 + r C.P. 100 − D
Correct Option: B
Here , marked price of a radio = ₹ 4,800 , discount = 10% and gains = 8%
Let CP of radio be Rs. y.
According to the question,108y = 4800 × 90 = 4320 100 100 ⇒ y = 4320 × 100 = ₹ 4000 108
Gain = 4800 - 4000 = ₹ 800
If no discount is allowed,thenGain percent = 800 × 100 = 20% 4000
Second method :
Given Here , M.P. = ₹ 4800, D = 10%, r = 8%
With the help of given formula ,M.P. = 100 + r C.P. 100 − D 4800 = 100 + 8 C.P. 100 − 10 C.P. = 4800 × 90 = 4000 108 Gain % (without discount) = 4800 − 4000 × 100 4000 Gain % = 800 × 100 = 20% 4000
- 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
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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, then11200 × 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, then11200 × 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%
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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 ?
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Let C.P. of article = ₹ 100
Marked price = ySingle 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 = ySingle 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 = 60Required percent = 60 × 100 = 60% 100
