Question

when x is subtract fom each of 16 15 31 and 27.5.the number so obtain on this order, are proportion what is the the mean proportion between 2x and x-5
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Answer 1

Correct Question :- when x is subtract fom each of 16 15 31 and 27.5.the number so obtain on this order, are in continued proportion what is the the mean proportion between 2x and x-5 .

Answer :-

given that,

→ (16 - x) : (15 - x) :: (31 - x) : (27.5 - x)

so,

→ product of extreme = product of means

→ (16 - x)(27.5 - x) = (15 - x)(31 - x)

→ 440 - 16x - 27.5x + x² = 465 - 15x - 31x + x²

→ 440 - 43.5x = 465 - 46x

→ 46x - 43.5x = 465 - 440

→ 2.5x = 25

→ x = 10 .

then,

→ Mean proportion between 2x and (x - 5) = √{2x * (x - 5)} = √{2*10 * (10 - 5)} = √(20 * 5) = √100 = 10 (Ans.)

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