Question

a and b are inversely proportional to each other and are positive. If a increases by 100%, then b decreases by

Options

• 50%

• 75%

• 10%

• 200%

Answer 1

50%

Explanation:

a and b are inversely proportional

So, `" a"  alpha1/"b"⇒ "a"="k"/"b".`

⇒ ab = k , ..........(where k = constant)

`⇒"b"="k"/"a"`

when a is increases by 100%

`∴ "a"+"a"xx100/100=2"a".`

then, 2 a . b' = k.

`"b"' = "k"/2"a"`

% decrease in b = `(("b"-"b"')/"b")xx100`

`=(("k"/"a"-"k"/(2"a")))/("k"/"a")xx100`

= 50%