Question : When P is subtracted from each of the numbers 8, 6, 2 and 9, the numbers so obtained in this order are in proportion. What is the mean proportional between (3P - 6) and (9P - 4)?
Option 1: 26
Option 2: 28
Option 3: 29
Option 4: 24
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Correct Answer: 28
Solution :
According to the question,
$(8-P)(9-P)=(6-P)(2-P)$
$⇒72+P^2-17P=12+P^2-8P$
$⇒9P=60$
$⇒P=\frac{20}{3}$
Mean proportion between $(3P - 6)$ and $(9P - 4)$
= $\sqrt{(3P - 6)(9P - 4)}$
= $\sqrt{(3×\frac{20}{3} - 6)(9×\frac{20}{3} - 4)}$
= $\sqrt{14×56}$
= $28$
Hence, the correct answer is 28.
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