The manufacturer’s suggested retail price (MSRP) of a certain item is

The last part asks to calculate the difference in sales tax amount i.e [ 5% of purchase price at store A - 5% of purchase price at store B ]
After basic calculations one can easily find the purchase prices at store A and B.

The purchase price at store A = 72
Sales tax amount at store A = 5% of 72 = 3.60
The purchase price at store B = 70.2
Sales tax amount at store B = 5% of 70.2 = 3.51
5% of purchase price at store A - 5% of purchase price at store B = 3.60-3.51 = 0.09 (Ans)

Since everything increases/decreases in percentage terms, another method is to assume price as 100 and then multiply the final answer by 3/5 to adjust for 60.

Store A price = 100 + 20 = 120
Store B price = 100 + 30 - 13 = 117

Difference after incorporating sales tax and adjusting for 60 = 3 * (105/100) ( 3/5) = 189/100 = $1.89

Answer (D)

Hi Bunuel, VeritasprepKarishma,

I did not understand this part of the question: "what is the result when the total cost of the item at Store B is subtracted from the total cost of the item at Store A?" What is the 'total cost' referring to?

Total cost here is referring to the final price of A and B after applying the sales/taxes.

Thank you, abhimahna. I guess I was confusing it with cost price.

Solution:

The total cost of the item at store A is 60 x 1.2 x 1.05 = $75.60.

The total cost of the item at store B is 60 x 1.3 x 0.9 x 1.05 = $73.71.

Therefore, the difference is 75.60 - 73.71 = $1.89.

Answer: D

(MSRP) of a certain item is $60.

Store A: sells the item for 20 percent more than the MSRP => \(\frac{120}{100}\) * 60 = 72

Store B:regular price of the item is 30 percent more than the MSRP => \(\frac{130}{100}\) * 60 = 78

=>But Store B: sells the item for 10 percent less than the regular price: \(\frac{90}{100}\) * 78 = 70.2

Store A - Store B = 72 - 70.2 = 1.8

Sales tax: 5% of the purchase price.

=> 1.8 * \(\frac{5}{100}\) = 0.09

Total difference: 1.8 + 0.09 = 1.89

Answer D

I understood the math I needed to do for this question but how does anyone read the problem and then calculate the arithmetic by hand in less than 2 minutes?

Hello VeritasKarishma,

I took the "10 percent less than the regular price" to mean that 10 percent of the regular price was subtracted from the marked up price, similar to how one would interpret "5 dollars less than 10". I've seen other questions that require interpreting the "percent less" as a subtraction and not as a multiplier.
Could you please provide some insight into how to ascertain what warrants the subtraction of a percentage of something and what warrants the use of a multiplier?

What you did is correct. Multiplier and addition/subtraction are equivalent concepts. Look here:

MSRP is 60.
Marked up price of store B = 60 + 30% of 60 = 60 + 60*(30/100) = 60 * (1 + 3/10) = 60 * (13/10) = 78

Discounted price = 78 - 10% of 78 = 78 * ( 1 - 10/100) = 78*(9/10) = 70.2

The addition/subtraction leads up to the multiplier by algebraic manipulation. Depending on given data, one of the other method comes out to be easier.
For example, if I know the multiplication table of 13, I can arrive at 78 directly. If I don't, I know that 10% of 60 is 6 so 30% will be 18 and hence 30% more than 60 will be 78.
Similarly, for discounted price, I know 10% of 78 is 7.8. So subtracting that from 80 gives me 70.2. This is easier than multiplying 78 with 9.

Multipliers are very useful in situations of successive percentage changes with suitable percentages. e.g. if there is an increase of 20% and a decrease of 37.5%, we will multiply by 6/5 and by 5/8 which will give A * (6/5)*(5/8) = A * (3/4) which is simply a decrease of 25% (an easier calculation)

Let MP = 60.
Selling price of A = A
Selling price of B = B

Now, A = 1.2*60 = 72
B = 1.3*60 = 78 but offers 10% off on B, therefore 78*0.9 = 70.2

Finally the sales tax is 5% meaning, the A and B both increase by 5 percent.

New A = 72*1.05
New B = 70.2*1.05

Difference = 1.05*(72-70.2) = 1.05*(1.8) = 1.89 = Ans

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