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Deepak Bora
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The sum of two numbers is 16 and the sum of their reciprocals is 1/3 Find the numbers.

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ICSE & CBSE Board Question Based on Linear Equations in two Variables of RS Aggarwal
Here the sum of two number and the sum of their reciprocals is given.
You have to find the number.
This is the Question Number 24 Of Exercise 3E of RS Aggarwal Solution.

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1 Answer

  1. Let one number be x.
    therefore , another number = 16 – x
    (because sum of two numbers is 16)
    also ,
    1/x + 1/16 – x = 1/3 (Given)
    16 -x +x / x(16 -x) = 1/3
    16*3 = x(16 – x)
    48 = 16x – x²
    or x² – 16x + 48 = 0
    or x² – 12x – 4x + 48 =0
    x(x-12) -4(x-12) =0
    x-4 = 0 or x-12 =0
    x=4 or x=12
    hence one Number is 4 .
    and another number = 16 – x =16 – 4 = 12 .

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