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Find the Whole Numbers Which When Decreased by 20 is Equal to 69 Times the Reciprocal of the Members. - CBSE Class 10 - Mathematics

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Question

Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.

Solution

Let the whole number be x as it is decreased by 20

⇒ (x - 20) = 69. (1/2)

⇒ 𝑥. 20 = 69. (1/𝑥)

⇒ 𝑥(𝑥 - 20) = 69

⇒ 𝑥2 - 20𝑥 - 69 = 0

⇒ 𝑥2 - 23 + 3𝑥 - 69 = 0

⇒ 𝑥(𝑥 - 23) + 3(𝑥 - 623) = 0

⇒ (x - 23) (x + 3) = 0

⇒ x = 23; x = -3

As the whole numbers are always positive, x = -3 is not considered.

∴ The whole number x = 23.

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Solution Find the Whole Numbers Which When Decreased by 20 is Equal to 69 Times the Reciprocal of the Members. Concept: Solutions of Quadratic Equations by Factorization.
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