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

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Math Expert
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If P > 0 and P % of 3P is P % less than P, then P equals:  [#permalink]

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New post 08 May 2018, 01:23
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

62% (01:45) correct 38% (02:32) wrong based on 82 sessions

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Re: If P > 0 and P % of 3P is P % less than P, then P equals:  [#permalink]

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New post 08 May 2018, 02:57

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 [(P – 3P^2/100)/P] * 100 = P
    Solving, we can get P = 25

Hence, the correct answer is option B.

Answer: B
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Re: If P > 0 and P % of 3P is P % less than P, then P equals:  [#permalink]

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New post 23 May 2018, 20:57
2
As per P % of 3P is P % less than P,

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

Solve P we get P=25

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Re: If P > 0 and P % of 3P is P % less than P, then P equals:  [#permalink]

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New post 01 Aug 2019, 12:11
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=\(\frac{1}{4}\)
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Re: If P > 0 and P % of 3P is P % less than P, then P equals:  [#permalink]

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New post 06 Aug 2019, 17:45
Bunuel wrote:
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


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
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Re: If P > 0 and P % of 3P is P % less than P, then P equals:   [#permalink] 06 Aug 2019, 17:45
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