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)?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 28.
(8 - P)/(6 - P) = (2 - P)/(9 - P)
⇒ 72 - 8P - 9P + P2 = 12 - 6P - 2P + P2
⇒ 72 - 17P = 12 - 8P
⇒ 9P = 60
⇒ P = 60/9 = 20/3
⇒ 3P - 6 = 3(20/3) - 6 = 20 - 6 = 14
⇒ 9P - 4 = 9(20/3) - 4 = 60 - 4 = 56
Mean proportional = √(14 × 56) = √(142 × 22) = 14 × 2 = 28
Hence, the mean proportional between (3P - 6) and (9P - 4) is 28.