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Question

# In the equation a(b+a)=10, a is _____

A
Directly proportional to b
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B
Inversely proportional to b
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C
Not proportional to b
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D
(b) and (c) above.
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Solution

## The correct option is C Not proportional to bTwo variables are said to be in inverse proportion if the product of the two variables is constant. Given, a(b+a)=10 ⇒ab+a2=10 ⇒ab=10−a2, which is not a constant. So, 'a' and 'b' are not inversely proportional to each other. Two variables are said to be in direct proportion if their ratio is constant. Now, ab=10b(b+a), which is also not a constant. ∴ 'a' and 'b' are not in direct proportion. From the above two conditions we can say that 'a' is not in proportion with 'b'.

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