The two numbers whose mean proportion is 12 and the third proportional is 324, its value is? Option 1: 6 and 32 Option 2: 4 and 36 Option 3: 4 and 18 Option 4: 8 and 24

Answer: 4 and 36. Solution: Let the numbers be a and b. Mean proportional: √ab=12 ab=144. Third proportional: b^2/a=324. Substituting a=144/b gives b^3/144=324, so b^3=46656 and b=36, hence a=4.

Arithmetic

Ratio, Proportion & Variation

Medium

The two numbers whose mean proportion is 12 and the third proportional is 324, its value is?

6 and 32

4 and 36

4 and 18

8 and 24

✅ Correct Option: 2

Let the numbers be $a$ and $b$ .

Mean proportional: $\sqrt{ab}=12\Rightarrow ab=144$ .

Third proportional: $\frac{b^2}{a}=324$ .

Substituting $a=\frac{144}{b}$ gives $\frac{b^3}{144}=324$ , so $b^3=46656$ and $b=36$ , hence $a=4$ .

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