Question

Two positive numbers x and y are inversely proportional. If x increases by 20%, then percentage decrease in y is: (a) 15 , (b) 16^2/3, (c)17^11/9, (d) 25.

Answer 1

answer is (b) 16(2/3)

as x increased by 20 % and becomes x'
and let y increased and becomes y'
as
x' = x + x(20%)
x' = x + x(1/5)
x' = 6x/5
if x is now 6/5 times the original value
than y' = 5y/6....as x and y are inversely proportional to each other
now percentage increase in y is
$\frac{change \: in \: y}{y} \: \times 100$
change in y is

(current value)-(original value)
(y') -(y)
(5y/6) - y
-y/6
now
percentage increase in y is
$\frac{ \frac{ - y}{6} }{y} \times 100$
which is
- 100/6
-50/3
-16(2/3)
hope so this helps if any doubt you may reply