What should be subtracted so that 19/28 55 91 are in proportion?

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| When x is subtracted from each of 19, 28, 55 and 91, the numbers so obtained in this order, are in proportion. What is the mean proportional between (x + 9) and x2?

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Right Answer is: C

Given -

When x is subtracted from each of 19, 28, 55, 91, obtained numbers are in proportion.

Concept used -

by componendo and dividendo

(a/b) = (x/y)

{(a + b)/(a - b)} = {(x + y)/(x - y)}

Solution -

19, 28, 55, 91

⇒ {(19 - x)/(28 - x)} = {(55 - x)/(91 - x)

⇒ By C and D method,

⇒ {(47 - 2x)/(- 9)} = {(146 - 2x)/(- 36)}

⇒ 188 - 8x = 146 - 2x

⇒ 6x = 42

⇒ x = 7

⇒ mean proportional = √{7 + 9) × 72} = 28

∴ mean proportional = 28.

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