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

MCQ

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

• 50%

• 75%

• 10%

• 200%

#### 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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