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A trader allows a discount of 10% on the marked price of an article and thus gains 17% on the cost price of the article. If the cost price is increased by 10%, then what percentage discount should he allow on the marked price of the article so as to get the same percentage profit as before?
- a)7
- b)5
- c)3
- d)1
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A trader allows a discount of 10% on the marked price of an article a...
Given:
Discount = 10%
Profit = 17%
Let the cost price of the article be Rs. x and the marked price be Rs. y.
Profit = Selling Price - Cost Price
17% = (y - 0.1y) - x
17% = 0.9y - x
0.9y = 17% + x
y = (100/90)*(17% + x)
y = (187/180)*x
Now, let the new cost price be 110% of the original cost price i.e. Rs. 1.1x.
Profit = Selling Price - Cost Price
Let the new discount be d.
17% = (y - d/100*y) - 1.1x
17% = (1 - d/100)*(187/180)*x - 1.1x
17% = (1 - d/100)*(187/180)*x - (11/10)x
17% + (11/10)x = (1 - d/100)*(187/180)*x
(17/100)*(10/11)*x + x = (1 - d/100)*(187/180)*x
(17/1100)*x + x = (1 - d/100)*(187/180)*x
(1100/1100)*(17/1100)*x + (1100/1100)*x = (1 - d/100)*(187/180)*x
(17/1100)*x + (1100/1100)*x = (1 - d/100)*(187/180)*x
(1117/1100)*x = (1 - d/100)*(187/180)*x
(1117/1100) = (1 - d/100)*(187/180)
d/100 = 1 - (1117/1100)*(180/187)
d/100 = 1 - 0.9176
d/100 = 0.0824
d = 8.24%
Therefore, the trader should allow a discount of 8.24% on the marked price of the article to get the same percentage profit as before. Hence, option D is the correct answer.
Discount = 10%
Profit = 17%
Let the cost price of the article be Rs. x and the marked price be Rs. y.
Profit = Selling Price - Cost Price
17% = (y - 0.1y) - x
17% = 0.9y - x
0.9y = 17% + x
y = (100/90)*(17% + x)
y = (187/180)*x
Now, let the new cost price be 110% of the original cost price i.e. Rs. 1.1x.
Profit = Selling Price - Cost Price
Let the new discount be d.
17% = (y - d/100*y) - 1.1x
17% = (1 - d/100)*(187/180)*x - 1.1x
17% = (1 - d/100)*(187/180)*x - (11/10)x
17% + (11/10)x = (1 - d/100)*(187/180)*x
(17/100)*(10/11)*x + x = (1 - d/100)*(187/180)*x
(17/1100)*x + x = (1 - d/100)*(187/180)*x
(1100/1100)*(17/1100)*x + (1100/1100)*x = (1 - d/100)*(187/180)*x
(17/1100)*x + (1100/1100)*x = (1 - d/100)*(187/180)*x
(1117/1100)*x = (1 - d/100)*(187/180)*x
(1117/1100) = (1 - d/100)*(187/180)
d/100 = 1 - (1117/1100)*(180/187)
d/100 = 1 - 0.9176
d/100 = 0.0824
d = 8.24%
Therefore, the trader should allow a discount of 8.24% on the marked price of the article to get the same percentage profit as before. Hence, option D is the correct answer.
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Community Answer
A trader allows a discount of 10% on the marked price of an article a...
Given:
Discount of 10% on the marked price.
Gains 17% on the cost price.
Again, cost price is increased by 10%.
Formula used:
Profit% = SP − CP / CP × 100
SP = MP - discount% on SP
Discount% = MP − SP / MP × 100
Let CP of the article be Rs. 100
SP of the article = 100 × 117 / 100 = 117
MP of the article = 117 × 100 / 90 = 130
New CP of the article = 100 × 110 / 100 = 110
New SP of the article = 110 × 117 / 100 = 128.7
Discount percentage = 130 − 128.7 / 130 × 100
⇒ 1.3 / 130 × 100 = 1%
∴ The answer is 1%.
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A trader allows a discount of 10% on the marked price of an article and thus gains 17% on the cost price of the article. If the cost price is increased by 10%, then what percentage discount should he allow on the marked price of the article so as to get the same percentage profit as before?a)7b)5c)3d)1Correct answer is option 'D'. Can you explain this answer?
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