Question : Find the third proportion of P and 12, when 8, P, 16, and 18 are in proportion.
Option 1: 16
Option 2: 8
Option 3: 18
Option 4: 12
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Correct Answer: 16
Solution : Given, $8, \mathrm{P}, 16$, and 18 are in proportion. So, 8 : $P$ :: 16 : 18 ⇒ $\frac{8}{P}=\frac{16}{18}$ ⇒ $P=9$ Now, third proportional to $a$ and $b$ is given by $\frac{b^2}{a}$, where $a$ = 9, $b$ = 12. So, the third proportional to 9 and 12 is = $\frac{12^2}{9}$ = $16$ Hence, the correct answer is 16.
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