Question

q as a percentage of p is equal to p as a percentage of (p + q). find q as a percentage of p. *

Answer 1

Given, Q as a percentage of p is equal to p as a percentage of (p + q)

i.e., (q/p) * 100 = (p/(p+q))*100 or q/p = p/(p+q)---I

as q is some percentage of P, lets take q = kp ----II

putting II in I  we get,

kp/p = p/(p+kp) or k = 1 / (1+k) ----III

Solving the quadratic eqn, k^2 + k-1 =0

we get k = -1 + √5 or k= -1 - √5

k=1.24/2 or -3.24/2-----IV

ignore the -ve value. Applying I in  q as % of p = q/p *100 = kp/p * 100 = k*100

Thus from Iv, q as % of p=(1.24 / 2) * 100 = 62%

Answer 2

Answer:

q as % of p = ($\frac{1.24}{2}$) × 100 = 62%

Step-by-step explanation:

Given, Q as a percentage of p is equal to p as a percentage of (p + q)

that is, $\frac{q}{p}$ × 100 = ($\frac{p}{p+q}$) × 100 or  $\frac{q}{p}$  =  $\frac{p}{p+q}$         ----------------------(1)

as q is some percentage of P, lets take q = k p -----------(2)

putting (2) in (1) we get,

$\frac{kp}{p}$ = $\frac{p}{p+kp}$  or k = $\frac{1}{k+1}$ ----------------(3)

Solving the quadratic equation, k² + k - 1 =0

we get k = -1 + √5 or k= -1 - √5

k = $\frac{1.24}{2}$ or $\frac{-3.24}{2}$-----------------------(4)

ignore the -ve value.

Applying 1 in  q as % of p = $\frac{q}{p}$ × 100 = $\frac{kp}{p}$ × 100 = k × 100

Thus from (4),

q as % of p = ($\frac{1.24}{2}$) × 100 = 62% .