If P 0 and P % of 3P is P % less than P, then P equals:

Question

If P > 0 and P % of 3P is P % less than P, then P equals:

A. 5

B. 25

C. 40

D. 50

E. 64

EgmatQuantExpert · Answer

Solution

Given:  
• P > 0
• P% of 3P is P% less than P

To find:  
• The value of P

Approach and Working:   
• P% of 3P =  \frac{P}{100} * 3P = \frac{{3P^2}}{100} 
 o Now this less than P by (P –  \frac{{3P^2}}{100} ) 
 o In terms of percentage, it is equal to   * 100 = P 
 Solving, we can get P = 25

Hence, the correct answer is option B.

Answer: B

push12345 · Answer

As per P % of 3P is P % less than P,

P*3P/100=P(1-(P/100))

Solve P we get P=25

Give kudos if it helps

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Xin Cho · Answer

I am not entirely sure whether I correctly converted the second half of the equation. I did the following:

\frac{P}{100} *3P= \frac{1-P}{100} *P

From there:

3P^2 =(1-P)*P
 3P^2 =P- P^2 
 4P^2 =P
P= \frac{1}{4}

ScottTargetTestPrep · Answer

Just as we can express 5% as 5/100, we can express P% as P/100. Doing so, we can create the equation:

P/100 * (3P) = (100 - P)/100 * P

3P^2/100=(100P - P^2)/100

3P^2 = 100P - P^2

4P^2 - 100P = 0

4P(P - 25) = 0

P = 0 or P = 25

Since we are given that P > 0, then P must be 25.

Answer: B

kjchiang3 · Answer

Made the same mistake as you here, as P% less than P should be formulized as:

1 - (P/100)

Not (1-P)/100.

Doing it the correct first formula results in the answer 25.

Abhishek009 · Answer

P % of 3P is P % less than P

So,  \frac{p*3p}{100} = \frac{(100 - p)p}{100}

Or,  3p^2 = 100p - p^2

Or,  4p^2 = 100p

Or,  4p = 100

Or,  p = 25 , Answer must be (B)

adityasuresh · Answer

If P > 0 and P % of 3P is P % less than P, then P equals:

A. 5

B. 25

C. 40

D. 50

E. 64

P/100  * 3P = P(1 -  P/100 )
 3P^2/100  = P -  P^2/100 
 4P^2/100  = P (Divide both sides by P)
 4P/100  = 1
P = 25

B

Stratos25 · Answer

why the square (^2) in the equation?

adityasuresh · Answer

Because P% OF 3P Translates as P/100 * 3P (OF implies multiplication)
so P * 3P = 3P^2 The whole divided by 100 = 3P^2/100
Similarly P% less than P translates as P(1 - P/100) (Less implies 1 - )
Simplifying P - P^2/100
3P^2/100 = P - P^2/100
3P^2/100 + P^2/100 = P (Divide both sides by P)
4P/100 = 1
P = 25

Hope its clear.

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If P > 0 and P % of 3P is P % less than P, then P equals:

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If P > 0 and P % of 3P is P % less than P, then P equals:

Prep Toolkit

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