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Q.

In inverse proportion, what is the relation between a 1 a 2 and b 1 b 2 and ?


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a

a 1 a 2 < b 2 b 1

b

a 1 a 2 > b 2 b 1

c

a 1 a 2 = b 2 b 1

d

a 1 a 2 ≤ b 1 b 2  

answer is C.

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Detailed Solution

Given that two quantities a and b are inversely proportional.
We know that two variables are said to be inversely proportional if and only if they are directly proportional to one another's reciprocal. If x and y are two variables in inverse variations, then
    x∝ 1 y ⇒x=k 1 y ⇒x= k y ,        where k is proportianality constant ⇒xy=k                                                   ....(1)
The product of the respective values of the two quantities is constant if two quantities vary inversely.
Apply this idea to determine the proper relationship between the provided quantities.
Given that two quantities are inversely proportional.
Then
a 1 b 1 =k             for some constant k
Similarly,
a 2 b 2 =k
 From the above two equations:
a 1 b 1 = a 2 b 2 ⇒ a 1 a 2 = b 2 b 1
Therefore, in inverse proportion, a 1 a 2 = b 2 b 1 .
Hence, option (3) is correct.
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