Question

two positive numbers x and y are inversely proportional if x increases by 20% then percentage decrease in y.

Answer 1

For inversely proportional numbers,product of number must be constant.

xy = const. equation(10

let, x and y both 20

then 20×20 = 400=constant

if x increases by 20 percent then the new value of x will be 24

From equation (1)

24×y =400

y = 400÷24

And now, in percentage decrease in y

[(20 - 400/24 )/20]×100 = 16.666 percent

Answer 2

Method - (1):

As we know that for a inversely proportional number, the product must be constant.

= > Let xy = k

Given that x is increased by 20% and y is decreased by a%.

= > (x + 0.2x) (y - (a/100) * y) = k

= > 1.2x * y(1 - a/100) = k

= > 1.2x * y(1 - a/100) = xy(from (1))

= > 1.2(1 - a/100) = 1

= > (1 - a/100) = (5/6)

= > 1 - a/100 = 5/6

= > - a/100 = (5/6) - 1

= > -a/100 = -1/6

= > a/100 = 1/6

= > 6a = 100

= > a = 100/6

= > a = 16.6667

= > a = 16 (2/3)%.

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Method (2):

xy = constant

Given that x increases by 20%.

= > % decrease in y = (20/100 + 20) * 100%

= > (20/120) * 100%

= > (50/3)%.

= > 16 (2/3)%.

Hope this helps!