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The variable x is inversely proportional to y. If x increases by p%, then by what percent will y decrease?

Solution:

If variable x is inversely proportional to y then

x ∝ 1/y

x = k/y

k = xy

So if x increases by p% then it will become:

x + px/100

x(1 + p/100)

Let y become y’ after x increases by p percent.

x(1 + p/100) × y’ = k

k = xy

x(1 + p/100) × y’ = xy

y’ = xy/x(1 + p/100)

y’ = y/(1 + p/100)

There y will decrease by:

y - y/(1 + p/100)

=(y + py/100 - y)(1 + p/100)

= (py/100)/(1 + p/100)

= py/(100 + p)

The percentage decrease in y will be:

[py/(100 + p)]/y × 100

100p/(100 + p) %

✦ Try This: The variable x is inversely proportional to y. If x decreases by p%, then by what percent will y increase?

If variable x is inversely proportional to y then

x ∝ 1/y

x = k/y

k = xy

So if x decreases by p% then it will become:

x - px/100

x(1 - p/100)

Let y become y’ after x decreases by p percent.

x(1 - p/100) × y’ = k

We know that k = xy

x(1 - p/100) × y’ = xy

y’ = xy/x(1 - p/100)

y’ = y/(1 - p/100)

There y will increase by:

y/(1 - p/100) - y

= [y - y(1 - p/100)]/(1 - p/100]

= (py/100)/(1 - p/100)

= py/(100 - p)

The percentage increase in y will be:

[py/(100 - p)]/y × 100

100p/(100 - p) %

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13

NCERT Exemplar Class 8 Maths Chapter 10 Problem 100

The variable x is inversely proportional to y. If x increases by p%, then by what percent will y decrease

Summary:

The variable x is inversely proportional to y. If x increases by p%, then y will decrease by 100p/(100+p) %

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