Q as a percentage of P is equal to P as a percentage of (P + Q). Find Q as a percentage of P?a.None of theseb.62%c.65%d.50%

Let's solve this step by step:

1. The problem states that "Q as a percentage of P is equal to P as a percentage of (P + Q)". We can express this as an equation:

   Q/P = P/(P + Q)

2. To solve for Q, we can cross-multiply:

   Q*(P + Q) = P*P

3. Simplifying this gives:

   QP + Q^2 = P^2

4. Rearranging terms, we get:

   Q^2 + QP - P^2 = 0

5. This is a quadratic equation in the form of ax^2 + bx + c = 0, where x is Q, a is 1, b is P, and c is -P^2. We can solve for Q using the quadratic formula:

   Q = [-b ± sqrt(b^2 - 4ac)] / (2a)

6. Substituting the values, we get:

   Q = [-P ± sqrt(P^2 - 41(-P^2))] / (2*1) Q = [-P ± sqrt(P^2 + 4P^2)] / 2 Q = [-P ± sqrt(5P^2)] / 2

7. Since Q cannot be negative, we discard the solution with the negative sign:

   Q = [-P + sqrt(5P^2)] / 2 Q = [sqrt(5P^2) - P] / 2

8. To find Q as a percentage of P, we divide Q by P and multiply by 100:

   Q/P * 100 = {[sqrt(5P^2) - P] / 2P} * 100 Q/P * 100 = {[sqrt(5) - 1] / 2} * 100

9. Simplifying this gives approximately 62%.

So, the answer is (b) 62%.