Question

The variable x is inversely proportional to y. If x increase by P%, then by what per cent will y decrease?

[2 marks]

Answer 1

The variable x is inversely proportional
$\therefore$ xy = k (constant)...(i)

[0.5 mark]

Since we know that two quantities x and y are said to be in inverse proportion.
Value of x after p% increase
$=x+\frac{P}{100}\times x$
Let Q% be the decrease in y, new value of y
$=y-\frac{Q}{100}\times y$

[0.5 mark]

From (i) we know that
($x+\frac{P}{100}\times x$)$\times$($y-\frac{Q}{100}\times y)=k$
On simplifying the above expression, we get
$Q=\frac{Py}{100+P}$

Increase in x causes a decrease in y and vice -versa.
So we can say y decrease by Q% i.e
$\frac{Py}{100+P}$%

[1 mark]