Increasing the original price of an article by 15 percent

Question

Increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by

A) 32.25%
B) 31.00%
C) 30.25%
D) 30.00%
E) 22.50%

Bunuel · Accepted Answer

You can do this by approximation, or with straight math by calculating 100*1.15^2.

Or step by step: if you increase 100 by 15% you'll get 115, then if you increase 115=100+15 by 15% again, 100 will gain 15 again and 15 will gain its 15% which is 2.25, so total gain is 15+2.25=17.25 --> 115+17.25=132.25.

Answer: A.

chiccufrazer1 · Answer

Increasing the original price of an article by 15% and then increasing the new price by 15% again is equivalent to increasing the original price by what %?

A. 34 
B. 40 
C. 68 
D. 88 
E. 102

Hey guys this might be as simple as abc for a math problem to you but not me..anyway this is how i did it after reading a gmat study guide on percents from platinumgmat albeit i dd not pretty well understand it..the two percentages in decimal form,will be as 0.15 each..x(0.15)multiply(0.15) the result is 1.3325x..to one decimal place it is 1.3x..i then found the percentage increase {(end value - start value)/start value)}*100 hence {(1.3225x-x)/x)}*100 =32.25 (to the nearest whole number;32..but among the answer choices there is no 32)how did i get it wrong?please help

MacFauz · Answer

To INCREASE a certain number by 15%, you will have to multiply by 1.15
To DECREASE a certain number by 15%, you will have to multiply by 0.85.
To find what 15% of a certain number is, you will have to multiply by 0.15

Lets say the original price of the article is 10$
Multiplying 10 by 1.15 we get 11.5$
Now multiplying 11.5 by 1.15 again we get 13.225 which is the same as increasing 10 by 32%.
So the answer you got is correct.

If the answer choices aren't incorrect, you would be best served to choose the closest possible answer choice i.e. A and move on.

Bunuel · Answer

The actual increase would be a little more that 15 + 15 = 30%, only A fits. Similar questions to practice: on-the-first-of-the-year-james-invested-x-dollars-at-128825.html marcus-deposited-8-000-to-open-a-new-savings-account-that-128395.html 10-000-is-deposited-in-a-certain-account-that-pays-r-65464.html john-deposited-10-000-to-open-a-new-savings-account-that-83953.html alex-deposited-x-dollars-into-a-new-account-126459.html a-total-of-60-000-was-invested-for-one-year-part-of-this-126655.html jolene-entered-an-18-month-investment-contract-that-127308.html You can find other question here; PS: search.php?search_id=tag&tag_id=191 DS; search.php?search_id=tag&tag_id=192 Hope it helps.

sandeepdey · Answer

During successive increment or decrements we can apply below mentioned logic. Helps to calculate faster

Let the price of a commodity is increased by a% and then b% then the final increment will be

1 + a/100 + b/100 + ab/10000

Now the same logic can be applied with decrements also with just changing the signs.
Let for example price of commodity is increased by a% and then decreased by b% then the resulting increase/decrease will be

1 + a/100 - b/100 -ab/10000

For the above question the approach will be

1 + 0.15 + 0.15 + 0.0225 = 1.3225 ==> 32.25% 
Closest answer is A

PareshGmat · Answer

Initial Price = 100

15% increase = 115

Again 15% increase on new price  = 115 + 115 * \frac{15}{100}

= 115 + 117.25

= 132.25

Percentage Increase = 132.25 - 100 = 32.25%

holeintheboat · Answer

Original Price be P

Increasing by 15% => New price = 1.15 P
Again Increasing it by 15 % => Final Price = 1.15*1.15 P = 1.3225 { 115^2 = 11*12  25  = 13225}

Hence increase is (1.3225 - 1)*100% = 32.25%

rhine29388 · Answer

consider base price as $100
15% increase = 1.15*100 = 115
Another 15% increase on new price = 1.15 * 115 = 132.25
therefore a 32.25% increase

Correct ans - A

larroulet · Answer

Lets say P=100 $ --> 100*15%=115$ = P1

115+15%*(115)= P2

You can think 115 as 100 + 10 + 5 and take 15% of each one:
15%* 100 = 15
15%*10= 1,5
15%*(2*5)=1,5-->15%*5=0,75

The answer is 115+15+1,5+0,75= 132,25 --> Answer A

Abhishek009 · Answer

Shortest method will be -

15 + 15 + \frac{(15*15)}{100}

= 30 + 2.25

= 32.25%

Hence, correct answer will be (A) 32.25%

singhabhijeet · Answer

Since the nearest ans to 32 % is option A. I chose option A.

Let 100 be original price. 
15 % increase = 115
15% increase = little more then 15 = 132

Hence 32 % increase.

Alternatively Solution  :

15 + 15 +  \frac{(15)(15)}{100}

30 + \frac{225}{100}

30 + 2.25

32.25

Hovkial · Answer

OFFICIAL GMAT EXPLANATION

If p is the original price, then the 15 percent increase in price results in a price of 1.15p. The next 15 percent increase in price results in a price of 1.15(1.15p), or 1.3225p. Thus, the price increased by 1.3225p – p = 0.3225p, or 32.25% of p. The best answer is A.

vigneshvrk · Answer

Let's assume the initial price is $100 and we increase it by 15%, which will be $15 and the total would be $115. Then we increase it again by 15% ---> $115*15% = $17.25
$115+$17.25 = $132.25

Hence the answer is 32.25%

Choice is A.

Kindly give kudos if correct.

ayakik · Answer

KarishmaB  This may be a very rudimentary question, and if so, I apologize in advance... But I originally got this wrong because I did 0.15*0.15 and got 0.0225, which clearly doesn't make sense. Can you please explain why this approach is incorrect? Is it because we have to take 15% of the resulting figure, not 15% of the 15% (which results in too small of a fraction)?

KarishmaB · Answer

15% of a number is a small part of it. 
For example, 15% of 100 is just 15.

But when we "increase a number by 15%" we are making it larger. 
We say this is 100 + 15/100 of 100 = 115

So when we want to "increase" a number by 15%, we multiply it by (1 + 15/100) i.e. by 115/100. The number increases. 
When we want to further increase it by 15%, we multiply it by another 115/100.

So we get N * 115/100 * 115/100 as the new number which is greater than the original. number N.

When we take N * 15/100 * 15/100, we are effectively finding the 15% of the 15% of the number. So if the number is 100, 15% of its 15% becomes 
15/100 * 15/100 * 100 = 2.25

ayakik · Answer

KarishmaB  This makes a lot of sense now. Thank you so much for the comprehensive explanation!

achloes · Answer

The 15% increase of x in the first round increases x by a certain amount. The 15% increase in the second round is applied to a higher number, so will yield a larger change.

ScottTargetTestPrep · Answer

This is a successive percent change problem. A common mistake is to add the two 15% increases and conclude that the overall increase is 30%. That doesn't work because the second 15% increase is applied to the  new  price, not the original price. We need to apply each increase one at a time.

Let's say the original price is $100. (We can pick any starting value, but $100 makes percent calculations easy.)

Step 1: Apply the first 15% increase. 
To increase a value by 15%, we multiply it by (100 + 15)/100 = 115/100 = 1.15.
$100 × 1.15 =  $115

Step 2: Apply the second 15% increase to the new price. 
Now we increase $115 by 15%:
$115 × 1.15 =  $132.25

Step 3: Determine the overall percent increase. 
The price went from $100 to $132.25, so the overall increase is:
$132.25 - $100 = $32.25
Since our starting value was $100, the overall percent increase is simply  32.25% .

Answer: A
 
 Takeaway:  When a value undergoes successive percent changes, multiply the individual multipliers together. Never simply add the percentages — that only works if each increase is applied to the  same  base, which it isn't in successive changes.

Increasing the original price of an article by 15 percent

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