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Sum of Two Numbers is 16. the Sum of Their Reciprocals is 1/3. Find the Numbers. - CBSE Class 10 - Mathematics

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Question

Sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.

Solution

Given that the sum of two numbers is 16.

Let the two numbers be x and 16 - x

By the given hypothesis, we have

`rArr1/x+1/(16-x)=1/3`

`rArr(16-x+x)/(x(16-x))=1/3`

⇒ 48 = 16x - x2

⇒ 𝑥2 - 16𝑥 + 48 = 0

⇒ 𝑥2 - 12𝑥 - 4𝑥 + 48 = 0

⇒ x(x - 12) - 4(x - 12) = 0

⇒ (x - 12) (x - 4) = 0

⇒ x = 12 or x = 4

∴ The two numbers are 4 and 12.

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Solution Sum of Two Numbers is 16. the Sum of Their Reciprocals is 1/3. Find the Numbers. Concept: Solutions of Quadratic Equations by Factorization.
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