When x is added to each of 9, 15, 21 and 31, the numbers so obtained are in proportion. What is the mean proportional between the numbers (3x–2) and (5x+4) ?
Answer & explanation
Correct answer: option 3
ATQ ,
⇒ \(\frac{9 + x}{15 + x}\) = \(\frac{21 + x}{31 + x}\)
Using componendo and dividendo
⇒ \(\frac{(15 + x)\;+\;(9 + x)}{(15 + x)\;-\;(9 + x)}\) = \(\frac{(31 + x)\;+\;(21 + x)}{(31 + x)\;-\;(21 + x)}\)
⇒ \(\frac{24 + 2x}{6}\) = \(\frac{52 + 2x}{10}\)
⇒ 60 + 5x = 78 + 3x
⇒ x = 9
⇒ Mean proportional of a and b = \(\sqrt {(a)(b)}\)
⇒ Mean proportional = \(\sqrt {(3x - 2)(5x + 4) }\) = \(\sqrt {25 \times 49}\) = 35