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Question
What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion?
Solution
Let x be added to each number then
16 + x, 26 + x and 40 + x
are in continued proportion.
⇒ `(16 + x)/(26 + x) = (26 + x)/(40 + x)`
Cross Multiplying
(16 + x) (40 + x) = (26 + x) (26 + x)
⇒ 640 + 16x + 40x + x2 = 676 + 26x + 26x + x2
⇒ 640 + 56x + x2 = 676 + 52x + x2
⇒ 56x + x2 - 52x - x2 = 676 - 640
⇒ 4x = 36
⇒ x = `(36)/(4)` = 9
∴ 9 is to be added.
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