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
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Here it is given P% of 3P is P% less than P,

i.e we have \(\frac{P}{100} * 3P =\) \(P-(\frac{P}{100} * P)\)

or \(3P^2 =\) \(100P - P^2\)

OR \(4P = 100\)

OR \(P =25\) i.e option B
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P-(\frac{P}{100} * P)
how you figured out this RHS like that?

If P% less than P meant.

P - (p/100)* p

What does P% more than P mean??
would that equal to P + (P/100)*P

thanks

An alternative approach to the problem should the direct translation prove difficult is to use the choices and backsolve. When backsolving always attempt to logically eliminate any impossible choices. In this case, it might be possible to eliminate the largest two choices since, 50% of 3 x 50 would be a value larger than P itself and thus not satisfy the conditions of the problem.

Then we can take the middle remaining choice, in this case choice B 25 and walk through the steps to see if it matches the conditions of the problem. So, use the provided calculator to determine that 25% of 75 = 18.75. Now, check to see if 18.75 is 25% less than 25 by using the percent change formula which is (difference/original) x 100. In this case the difference is 6.25 and the original would be our plugged in value of p which is 25. 6.25 ÷ 25 = 0.25 x 100 = 25%, therefore choice B 25 matches all conditions of the problem and is the correct choice.