In the year-end clearance sale, a music system is discounted by d%

Hi Sandeep,

It would probably be a bit too soon to comment, since the explanation is yet to be made available, but here is what I think should be looked into.

After reviewing the OA, which is 'D', and working through the question, here is what I think should be modified.

If you review the question stem, you should see it says the following "...another 3d% on the previous discounted amount...". Here, discounted amount is a bit ambiguous, since it conveys that we are referring to the final amount after applying the discount. If you were to calculate the answer the way I did, you would end up with 'E'. Whereas, if the discount would have been applied on the discount amount, the answer would be 'D'.

My 2 cents here would be that we modify the question statement to say, '...discount amount...' instead of '...discounted amount...'.

Hope this helps to clarify. Please keep me posted as to what are your thoughts on this as well.

Best,
Sayan

Solution

Given:

• In the year-end sale, a music system is first discounted by d%
• And, then it is discounted by another 3d% on the initial discount amount
• d = 30%

To find:

• % of Original Price/Final Price

Approach and Working:

• Let us assume that the Original Selling Price is S

o Then, the selling price after the first discount of \(d% = S – S*\frac{d}{100}\)

• Now, a discount of 3d% is given on the previous discounted amount, that is \(S*\frac{d}{100}\)

o Thus, the final price of the music system = \(S – S*\frac{d}{100} – S * (\frac{d}{100}) * (\frac{3d}{100})\)

• Therefore, the percentage of original price by final price = \(\frac{S}{[ S – S*d/100 – S * (d/100) * (3d/100)]} *100 = \frac{1}{[ 1 – d/100 – (d/100) * (3d/100)]} * 100\)

o Substituting the value of d as 30 in the above equation, we get the percentage value = \(\frac{100}{[1 – 0.3 – 0.3*0.9]}= \frac{100}{(1 - 0.57)} = \frac{100}{0.43} ≃ 233%\)

Hence, the correct answer is option D.

Answer: D

Hey Sayan,

Thanks for pointing it out. Yes the word "discounted amount" is a bit ambiguous, so we have changed it to "discount amount."

Regards,
Sandeep
e-GMAT

Thanks Sandeep, much appreciated!

Let original price be P.

1st,it is discounted by 30%---> new price =7P/10.

2nd ,7p/100 is discounted by 90%=> (1/10)*7P/10

Original/Final %=P/(1/10*7P/10)
=100/7

143%

What am i missing here?

You are taking into account the price after discount, however, it says that the second discount is on the discount amount and not the price after discount.
Hope I am able to resolve your query.

Hi,

I still cannot comprehend. Can you explain in detail, please??? I too arrived at 143%

question difficulty is based on the amount of confusion created

Let the original price be 100.

1st,it is discounted by 30%---> discount amount = 30

2nd ,90% on discount amount=> 30*(90/100) = 27

Final Price = original price - 1st discount amount - 2nd discount amount
= 100 - 30 - 27 = 43
Original Price = Final price * (x/100)
100 = 43*(x/100)
x = 10000/43 = ≃ 233%

wording of the question is what's making it confusing
let initial price be 100
given 1st discount 30%
so price after 1st discount 70
2nd discount is given at 90% of 1st discount amount which is 30 *.9 ; 27
new price 70-27 ; 43

original price of the music system is what percent of the final value

100/43 ; 233

option D

Could be solved under a minute if we use formula for successive discounts.

lets assume that the initial price is 100.

( a + b -ab/100)

a = 1st discount
b = 2nd discount

now (30 + 90 - 2700/100) = 93 (discount )

final price after 2 successive discounts is 100-93 = 7

now original price/ final price = (100/7) * 100 = 142%

100/7 equals 14.28, which is

1428%

However, this is not the correct approach, since the second discount is not applied to the initially discounted price but to the initial discount itself.

Posted from my mobile device

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This is not a case of successive discounts because the second discount 3d is applied to the first discount.
If we consider the selling price as 100 for our ease, then after the first discount of 30%, SP becomes 100-(30*100/100)=70 i.e. discount is $30.
Now, we have to apply the second discount of 3*30=90% on this $30 so the second discount is 30*90/100=27.
Therefore, we can write our final price is 100-30-27=43.
Let the final price is x% of the original SP i.e. 43*x/100=100 or, x=100*100/43=232.55~233%. Option (D) is correct.