A retail item is offered at a discount of p percent (where p

Let x be the price of the item.
Final price after discount and sales tax = x * (1 - p/100) * 1.05

Let q be the percent discount which would result in the same final price.
Then,
x * (1 - p/100) * 1.05 = x * (1 - q/100)
=> 1.05 - 1.05p/100 = 1 - q/100
=> q/100 = 1.05p/100 - .05
=> q = 1.05p - 5

Hence , option C is correct.
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Appreciate your KUDOS.

Assume p = 20 % and original price = 100. Thus, the discounted purchase price = 80 and the sales tax assessed on this is 5 % = 84. Thus, a 16 % discount on the original retail price would result in the same price. Only option C gives 16 % for p = 20.

C.
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So I initially approached it the way you all did but messed up the math as I tried to convert the 1.05 into a fraction over 100 on both sides.

Instead to stay within 2:30 I plugged and chugged
Original Price: 100
Discount: 10
Discounted Price: 90

Sales tax on 90 is 4.5. Final price is 94.5

To achieve this price without tax you need a discount of 5.5

The answer choices are nice too for plugging and chugging

p+5/1.05 too big approximately 15/1
p/1.05 +5 too big again
1.05p-5 10.5-5=4.5 exactly
p-5/1.05 5/1.05...slightly smaller than 5 but not by much. Not nearly as big as the denominator bring the value to half way between 4 and 5
1.05(p – 5) More than 5. In fact 5.25

Answer is C

Hi,

Please help me with understanding the question?
.
What does the second part of the question states " If the state sales tax were not assessed......"

My understanding is that for text ''if the sales tax were not assessed" mean tax is not charged that means the discounted purchase price would be

Discounted purchase price = 80 i.e. with out the 5% of tax in the discounted purchase price

Please help me.

Thanks in Advance,
Rrsnathan.

Original price = $100.
Discount = p = 20%.
Tax = 5%.

Final price = 100*0.8*1.05 = $84.

The question asks: if the tax were not assessed, what percent discount from the original price ($100) would result in the same final price of $84. The answer is 16%.

Does this make sense?
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Just a small tip...When plugging in always try the easier option first. A,B and D involve divsion whereas C and E involve only multiplication.

Original price = $100.
Discount = p = 20%.
Tax = 5%.

Final price = 100*0.8*1.05 = $84.

The question asks: if the tax were not assessed, what percent discount from the original price ($100) would result in the same final price of $84. The answer is 16%.

Does this make sense?

Bunuel,

How have you arrived at this-
Discount = p = 20%.

I assumed it, plugged smart numbers.
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Backsolving would be the best approach here using Smart Numbers
Original price = 100
p = 20%
Tax = 5%

Then reduced price after tax $84
So then we need 16% before taxes

Therefore,
Target 16
Input P = 20

Now, it would help if the answer choices are stated clearly as fractions but anyway the approach is clear

Hope it helps
Cheers!
J

Bunuel,

What do they mean by "If the state sales tax were not assessed" ? I took the final price as 80 thinking we need not include the sales tax to it !

Original price = $100.
Final price = $84.

The question basically asks about the actual discount on the item, which is 16%.
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But my doubt is how do we decide that "final price" is 84 which with the applied sales tax or jus 80 which is without sales tax?
What if the "If the state sales tax were not assessed" part is omitted?

Hi Bunnuel,

if 5% on 80 is assessed as sales tax then it should be 80-4 right?

why is it 80+4?

5% state sales tax is assessed on the discounted purchase price, so (final price) = (discounted purchase price)*1.05. How else?
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When we usually talk about taxes being applicable..they are applicable on both the Marked Price and the Discounted Price. The question should state that state sales tax is assessed on what and on what its not...ambiguous wording..

Understand the right answer is to plug in smart numbers. But could someone please show step by step on how to solve this algebraically? I can't seem to be able to get the right answer. Any help much appreciated ! Bunuel

Bunuel niks18 chetan2u





Let us say original price is 100 since i am dealing with %tages and discounts.

I can have all sort of combinations from :
100 * 1.07 * 1.05
to
100*1.02*1.05

In a PS problem, do I not need an unique value to proceed from here?
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Hi adkikani

Can you clarify what the highlighted number signify here and how you are proceeding with respect to the question. If you are assuming any value then you should stick with that value and solve the question. If for example you have assumed p as 7% or 2% (which is not possible in this case), then you should use any one of this value and solve the question. then check the option using the assumed values of p

Hi xnthic

Let the original price be 100, after discount of p% the price will be \(100-p\). Now sales tax of 5% is added to this price.

Hence final price will be \((100-p)*1.05\)------(1)

Now the second part of the question says that sales tax is not assessed, but the final price is same as (1). so let the new discount be \(y\),

Hence new price will be \(100-y\), this is same as (1), so we have

\(100-y=(100-p)*1.05 =>100-y=105-1.05p\)

therefore, \(y=1.05p-5\)