Question : The difference between 24 and the mean proportional of 7 and 63 is:
Option 1: 3
Option 2: 2
Option 3: 5
Option 4: 4
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Correct Answer: 3
Solution : Let $x$ be the mean proportion. $a=7,b=63$ For mean proportion: $\frac{a}{x}=\frac{x}{b}$ $⇒x^2 = a\times{b}$ $⇒x = \sqrt{7\times63}$ $⇒ x = \sqrt{441}$ $⇒x = 21$ $\therefore$ The difference between 24 and the mean proportional of 7 and 63 is $=24-21 = 3$ Hence, the correct answer is 3.
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