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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
29% (02:15) correct
71%
(02:30)
wrong
based on 113
sessions
History
Date
Time
Result
Not Attempted Yet
If the selling price of a mat is five times the discount offered and if the percentage of discount is equal to the percentage profit, find the ratio of the discount offered to the cost price.
(A) 11 : 30
(B) 1 : 5
(C) 1 : 6
(D) 7 : 30
(E) None of these
Are You Up For the Challenge: 700 Level Questions
(A) 11 : 30
(B) 1 : 5
(C) 1 : 6
(D) 7 : 30
(E) None of these
Are You Up For the Challenge: 700 Level Questions
06 Feb 2022, 01:08
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If the selling price of a mat is five times the discount offered and if the percentage of discount is equal to the percentage profit, find the ratio of the discount offered to the cost price.
Interesting question. First determine what exactly the question requires us to answer.
find the ratio of the discount offered to the cost price
Now we have two information to find this ratio
1 The selling price of a mat is five times the discount offered
2 The percentage of discount is equal to the percentage profit
from 1,
SP = 5* Discount offered
Instead of dealing with variables let us plug in numbers
SP=100
Discount=20
Plugging numbers is ok because we are working with ratios throughout the question.
So if selling price is 100 and discount is 20, we can get that the product was listed at 100+20=120
from 2,
Percentage of discount= Percentage of profit
Percentage of discount= \(\frac{discount}{listed price}*100 \)
= \(\frac{20}{120} *100 \) (from 1) // leave it in this form as the 100 will cancel later
We have percentage of profit and sp so we can find cp
cp(1+\(\frac{gain%}{100}\)) =sp
cp(1+\(\frac{ 20}{120}\))=sp // as promised the 100 has cancelled
cp= \(\frac{6}{7} *sp\) =\( \frac{600}{7}\)
Now we can find ratio of discount offered to cost price
discount offered= 20
cost price= \(\frac{600}{7}\)
ratio is 20 : \(\frac{600}{7 }\)
= 1 : \( \frac{30}{7}\)
= \(7:30\)
Hence D is correct.
Interesting question. First determine what exactly the question requires us to answer.
find the ratio of the discount offered to the cost price
Now we have two information to find this ratio
1 The selling price of a mat is five times the discount offered
2 The percentage of discount is equal to the percentage profit
from 1,
SP = 5* Discount offered
Instead of dealing with variables let us plug in numbers
SP=100
Discount=20
Plugging numbers is ok because we are working with ratios throughout the question.
So if selling price is 100 and discount is 20, we can get that the product was listed at 100+20=120
from 2,
Percentage of discount= Percentage of profit
Percentage of discount= \(\frac{discount}{listed price}*100 \)
= \(\frac{20}{120} *100 \) (from 1) // leave it in this form as the 100 will cancel later
We have percentage of profit and sp so we can find cp
cp(1+\(\frac{gain%}{100}\)) =sp
cp(1+\(\frac{ 20}{120}\))=sp // as promised the 100 has cancelled
cp= \(\frac{6}{7} *sp\) =\( \frac{600}{7}\)
Now we can find ratio of discount offered to cost price
discount offered= 20
cost price= \(\frac{600}{7}\)
ratio is 20 : \(\frac{600}{7 }\)
= 1 : \( \frac{30}{7}\)
= \(7:30\)
Hence D is correct.
20 Oct 2022, 22:33
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If the selling price of a mat is five times the discount offered and if the percentage of discount is equal to the percentage profit, find the ratio of the discount offered to the cost price.
(A) 11 : 30
(B) 1 : 5
(C) 1 : 6
(D) 7 : 30
(E) None of these
SP = 5 * Discount - Discount = \(SP/5\)
Discount % = Profit % = x %
Let C.P = 100
SP = 100 + x
Discount = 100 +\( x/5\)
MP = SP + Discount = SP + \(SP/5\) = \(6SP/5\)
Discount % = Profit %
\(SP/5/6SP/5\) * 100 = X
X = 100/6 = \(50/3\)% Required Profit %
Ratio of discount to CP
D:CP = 100+50/3/5 = \(350/5\) * \(1/3\) = \(70/3\)
70/3:100 = 70 : 300 = 7:30
D
(A) 11 : 30
(B) 1 : 5
(C) 1 : 6
(D) 7 : 30
(E) None of these
SP = 5 * Discount - Discount = \(SP/5\)
Discount % = Profit % = x %
Let C.P = 100
SP = 100 + x
Discount = 100 +\( x/5\)
MP = SP + Discount = SP + \(SP/5\) = \(6SP/5\)
Discount % = Profit %
\(SP/5/6SP/5\) * 100 = X
X = 100/6 = \(50/3\)% Required Profit %
Ratio of discount to CP
D:CP = 100+50/3/5 = \(350/5\) * \(1/3\) = \(70/3\)
70/3:100 = 70 : 300 = 7:30
D
