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Question
Which number should be subtracted from 12, 16 and 21 so that resultant numbers are in continued proportion?
Solution
Let the number x be subtracted from 12, 16 and 21 so that the resultant numbers are in continued proportion.
∴ (12 − x), (16 − x), (21 − x) are in continued proportion.
∴ `(12 − x)/(16 − x) = (16 − x)/(21 − x)`
∴ `((12 − x) - (16 - x))/(16 - x) = ((16 - x) - (21 - x))/(21 - x)` ...(Using Dividendo)
∴ `(12 - x - 16 + x)/(16 - x) = (16 - x - 21 + x)/(21 - x)`
∴ `(-4)/(16 - x) = (-5)/(21 - x)`
∴ −4 (21 − x) = −5 (16 − x)
∴ −84 + 4x = −80 + 5x
∴ −84 + 80 = 5x − 4x
∴ −4 = x
∴ x = −4
Thus, the number −4 must be subtracted from 12, 16 and 21 so that the resultant numbers are in continued proportion.
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