Which of the following gives the highest overall percent increase, if

Let the initial value be 100.
(A) 100 -> 110 -> 165, 65% increase.
(B) 100 -> 125 -> ~168.75, 68.75% increase.
NOTE: This can be calculated easily as follows.
30% increase: 125 -> 30% = 30%(100) + 30%(25) = 30 + 7.5 = 37.5.
5% increase: 125 -> 5% = 12.5/2 = 6.25
So total increase = 37.5 + 6.25 = 43.75

(C) 100 -> 130 -> 169, 69% increase.
(D) 100 -> 140 -> 168, 68% increase.
(E) 100 -> 145 ->166.75, 66.75% increase.

Ans - C.
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Let the number be \(100\).

Lets check the options;

(A) 10% increase followed by 50% increase \(= \frac{110}{100} * \frac{150}{100} * 100 = 165\)

(B) 25% increase followed by 35%increase \(= \frac{125}{100} * \frac{135}{100} * 100 = 168.75\)

(C) 30% increase followed by 30% increase \(= \frac{130}{100} * \frac{130}{100} * 100 = 169\) --------- Greatest value. Highest overall percent increase.

(D) 40% increase followed by 20 % increase \(= \frac{140}{100} * \frac{120}{100} * 100 = 168\)

(E) 45% increase followed by 15 % increase \(= \frac{145}{100} * \frac{115}{100} * 100 = 166.75\)

Answer (C)...

Evaluating answer options
(A) 10 percent increase followed by 50 percent increase = 1.1 * 1.5 = \(\frac{11}{10} * \frac{15}{10}= \frac{165}{100}\)
(B) 25 percent increase followed by 35 percent increase = 1.25 * 1.35 = \(\frac{125}{100} * \frac{135}{100} = \frac{168.75}{100}\)
(C) 30 percent increase followed by 30 percent increase = 1.3 * 1.3 = \(\frac{13}{10} * \frac{13}{10} = \frac{169}{100}\)
(D) 40 percent increase followed by 20 percent increase = 1.4 * 1.2 = \(\frac{14}{10} * \frac{12}{10} =\frac{168}{100}\)
(E) 45 percent increase followed by 15 percent increase = 1.45 * 1.15 = \(\frac{145}{100} * \frac{115}{100} = \frac{166.75}{100}\)

Since all the denominators are equal, the highest number must be greatest number
Hence, Option C is the correct answer.
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Anyone know of any shortcuts to solve to help avoid mistakes on 5 separate calculations?
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Use the formula of Successive Increase/Decrease

(A) \(10 + 50 + \frac{50*10}{100}\) = \(65\) %
(B) \(25 + 35 + \frac{25*35}{100}\) = \(68.75\) %
(C) \(30 + 30 + \frac{30*30}{100}\) = \(69\) %
(D) \(40 + 20 + \frac{40*20}{100}\) = \(68\) %
(E) \(45 + 15 + \frac{45*15}{100}\) = \(66.75\) %

Thus, the correct answer must be (C)
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This one's interesting - and can be done with very minimal calculation.

As Abhishek009 mentioned, formula for successive percentage increase, when a value is increased first by a% and then by b% is given by:

[ a + b + (a*b)/100 ]%

If we look at our options, in ALL cases, (a+b) is same --> 60

So our MAX answer will be the one where a*b is MAX, i.e., product is MAX. Here we can now check the options one by one to find that in case of C, product is highest --> 30*30 = 900.. OR we can even avoid this calculation if we apply the following property:

When sum of positive numbers is fixed, their product is MAX when they are equal ..

Here sum of a&b, (a+b) is fixed as 60.. so their product will be MAX when they are equal which is in case of option C.

C is therefore, the highest % increase and is our answer

Thank you for this.
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Which of the following gives the highest overall percent increase, if in each case, the second percent increase is applied on the value obtained after application of the first percent Increase?

Though I got the answer by the crude way or the traditional way of doing it, i liked the method mentioned by Abhishek009 of progressive increase or decrease.

Progressive increase \(= a + b + \frac{a*b}{100}\)

A - \(10 + 50 + 10*50/100\)
B - \(25 + 35 + 25*35/100\)
C - \(30 + 30 + 30*30/100\)
D - \(40 + 20 + 40*20/100\)
E - \(45 + 15 + 45*15/100\)

As we can see a + b is 60 and same for all 5 options, the only thing that will decide now is a*b

If a*b is maximum we would know that increase is highest

Scanning through the options we know that only C gives us the maximum value of 900 as compared to any other options.

Hence, Answer is C
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Let’s use a starting value of x:

A) 10 percent increase followed by 50 percent increase

(1.1)(1.5)x = 1.65x

B) 25 percent increase followed by 35 percent increase

(1.25)(1.35)x = 1.6875x

C) 30 percent increase followed by 30 percent increase

(1.3)(1.3)x = 1.695x

D) 40 percent increase followed by 20 percent increase

(1.4)(1.2)x = 1.68x

E) 45 percent increase followed by 15 percent increase

(1.45)(1.15)x = 1.6675x

We see that the largest answer is 1.695x.

Answer: C
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Option A: 110 * 150 = (130 - 20) * (130 + 20) = \(130^2 - 20^2\)
Option B: 125 * 135 = (130 - 5) * ( 130 + 5) = \(130^2 - 5^2\)
Option C: 130 * 130 = \(130^2\)
Option D: 140 * 120 = (130 + 10) * (130 - 10) = \(130^2 - 10^2\)
Option E: 145 * 115 = (130 + 15) * (130 - 15) = \(130^2 - 15^2\)

Definitely option C is greatest of all

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