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A and B Are Inversely Proportional to Each Other and Are Positive. If a Increases by 100%, Then B Decreases by - Mathematics

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MCQ

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%

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Solution

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%

Concept: Ratio and Proportion (Entrance Exam)
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