#### Question

Find the smallest number that must be subtracted from each of the numbers 20, 29, 84 and 129 so that they are in proportion.

#### Solution

Let x be subtracted from each number so that 20-x, 29-x, 84-x and 129-x are in proportion.

`therefore (20 - "x")/(29 - "x") = (84 - "x")/(129 - "x")`

⇒ (20 - x)(129 - x) = (29 - x)(84 - x)

⇒ 2580- 129x - 20x + x^{2} = 2436 - 84x - 29x + x^{2}

⇒ 2580 - 149x = 2436 - 113x

⇒ 36x = 144

⇒ x = 4

Hence, 4 is to be subtracted from 20, 29, 84 and 129 for them to be in proportion.

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Solution Find the Smallest Number that Must Be Subtracted from Each of the Numbers 20, 29, 84 and 129 So that They Are in Proportion. Concept: Proportions.