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Mathematics

What must be subtracted from each of 7, 9, 11 and 15, so that the resulting numbers are in proportion?

  1. 1

  2. 2

  3. 3

  4. 5

Ratio Proportion

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Answer

Let the number to be subtracted be x.

Thus, the numbers 7 - x, 9 - x, 11 - x and 15 - x are in proportion.

⇒7−x9−x=11−x15−x\Rightarrow \dfrac{7 - x}{9 - x} = \dfrac{11 - x}{15 - x}

⇒ (7 - x)(15 - x) = (11 - x)(9 - x)

⇒ 105 - 7x - 15x + x2 = 99 - 11x - 9x + x2

⇒ 105 - 22x + x2 = 99 - 20x + x2

⇒ 105 - 99 = 22x - 20x

⇒ 6 = 2x

⇒ x = 62\dfrac{6}{2}

⇒ x = 3.

Hence, option 3 is the correct option.

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