Question

The variable X is inversely proportional to Y if x increases by P percent then by what percent y will decrease

Answer 1

y is decreased by (p/(100+p))×100%

Answer 2

Answer:

100P/(100 + P)

Step-by-step explanation:

The variable X is inversely proportional to Y if x increases by P percent then by what percent y will decrease

X  ∝ 1/Y

X = a/Y

=> Y = a/X

if X i increased by P %

then

increased X1 = (a/Y)(1 + P/100)

X1 = (a/Y)(100+P)/100

New Y1 = a/(X1)

Y1 =  a/((a/Y)(100+P)/100)

=> Y1 = 100Y/(100+P)

Reduction in Y

Y - Y1

= Y - 100Y/(100+P)

= (100Y + PY - 100Y)/(100+P)

= PY/(100+P)

% Reduction in Y   = {(PY/(100+P))/Y } * 100  =  100P/(100 + P)