The original price of an article was reduced by 25%. During a special

Question

The original price of an article was reduced by 25%. During a special sale the new price was decreased by 10%. By approximately what percentage would the new price have to be increased in order to restore the price of the article to its original amount?

A. 32.5%
B. 35%
C. 48%
D. 65%
E. 67.5%

Show Answer

Official Answer

C

A. 32.5%
B. 35%
C. 48%
D. 65%
E. 67.5%

pips883 · Accepted Answer

The equation is: 
(3/4*9/10)*x=1

Where 3/4 = 25% decrease, 9/10 = the 10% decrease, x the increase we want to find to have the original price 100% or 1.

= (27/40)*x = 1
Cross multiply x = 40/27 
x = 1.481 or 48%.
 Answer C

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jwang516 · Answer

Note the question says "approximately". That tells me an exact solution may be difficult to come by without a calculator.

Plugging in numbers seems to be the easiest way to solve

Let Price = $100
Decrease by 25% = (1-.25) * 100 = 75
Decrease by another 10% = (1 - .10) * 75
Note this is the same as 75 - .1(75) = 75 - 7.5 (since 10% of 75 = 7.5) = 67.5

To get to the original price, we must calculate (100 - 67.5) = 32.5

32.5 / 67.5 is the change to the new price
Note that 32.5 * 2 = 65. Since 65 is just a little smaller than 67.5, this means that 32.5 is just a little bit less than 1/2 of 67.5 (This is where "Approximation" in the question comes in handy)

Looking at the answers, C is the just a little less than 50%
Therefore, the answer is C

HolaMaven · Answer

Even an easier way is eliminating the options.
25%+10% = 35%, too easy and not an answer
(100-35)% = 65%, again too easy
(100-25)% = 75% - 10%*75* = 67.5% Not possible as its only decrease
(100-67.5)%=32.5%, again not possible as this will increase value to 100% but we need to calculate % increase
Thus option C - 48%

pushpitkc · Answer

The best method for such questions is to work with numbers.
When choosing a number, make sure, that the number is easy to work with!

Let the original price of the of the item be 400$,
since there is a decrease of 25%, the price goes down to 300$.
Again, during the special sale(10% decrease) the price goes down to 270$(less by 30$ or 10%)

Since we need to find out by approximately what percentage the price needs to go up,
the percentage increase is  \frac{130}{270}*100 = \frac{1300}{27} = 48.14 = 48 % approximately(Option C)

generis · Answer

Expanding a bit on  pips883  's good answer, because this method is easier for me than picking numbers with percent change - a rare phenomenon.
 
Percentage increase and percentage decrease are inversely proportional.

To find percentage by which the changed number must increase or decrease to return to the original

1) Find the fraction for the first change 
2) Flip that fraction, and
3) Calculate decimal value. That's the answer.

Here the article was reduced in price twice, by 25 percent and then 10 percent of that.

First decrease = .75 or  \frac{3}{4} , and second decrease, taken with the first, = .90 or  \frac{9}{10}

Total decrease:  \frac{3}{4}  *  \frac{9}{10}  =  \frac{27}{40}

Flip that fraction:  \frac{40}{27}

\frac{40}{27}  = 1.481, approximately 48%

That's the percentage by which the reduced price must increase to return to original.

Answer C

**Or multiply the multipliers --> (.75)(.9) = .625. Change to fraction  \frac{625}{1000}  =  \frac{27}{40} . Flip and find decimal value.

pips883 · Answer

Completely agree on that. Actually, my first thought when solving this question was "Come on, pick 10 and do the math". Then I realized that would be much easier if I worked with fractions. So, 99.9% times I pick numbers, but sometimes algebra may be the easiest path.

By the way, thanks for clarifying my solution. It looks much better now.

Bounce1987 · Answer

Plugging in numbers should help.
3/4*9/10(1+x/100)=1 Answer C

sashiim20 · Answer

Let the original price be  = 100

Price was reduced by  25  %    = 75  %   of  100 = \frac{75}{100} * 100 = 75

During special sale price was further decreased by  10  %    = 90  %  of  75 = \frac{90}{100} * 75 = 67.5

Difference of Original price and final price  = 100 - 67.5 = 32.5

Required percent  =  (Difference  /  Final price ) *100

Required percent  = (\frac{32.5}{67.5}) * 100 = 48.148  %    =  Approximately  = 48  %

Also half or  50  %   of  67.5  or approximately  68  is  = 34

Therefore answer should be slightly less than  50  % . Percentage required  = 48  %

Answer (C)...

HolaMaven · Answer

Yes plugging is a good approach but before plugging in see if you can eliminate answer choice without really doing any calculation. Practice will make you build require confidence to work faster on eliminating answer choice which can help in rectifying casual errors also. Try to reduce your efforts on easy questions so that you can concentrate better on trickier ones.

JeffTargetTestPrep · Answer

Let’s let the original price of the article be 100. In the first reduction, it was reduced by 25% and thus becomes 75. In the second reduction, it was reduced by 10% and thus becomes (0.9)(75) = 67.5. We note that the price must increase by 32.5 to be restored to the original price, and 32.5 is very close to, but less than, half of 67.5; therefore, the answer must be very close to, but less than, 50%. Scanning the answer choice, 48% fits our criteria.

Answer: C

Abhishek009 · Answer

Net discount during special sale is  -25 - 10 + \frac{(-25)(-10)}{100} = -35 + 2.50 = -32.50

So, The price of the article must is  100 - 32.50 = 67.50

Thus, the final price must be restored by  \frac{32.50}{67.50}*100  ~  48  %, Answer must be (C)

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