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Question -

The sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers. (C.B.S.E. 2005)



Answer -

Sum of two numbers = 16
Let first number = x
Then second number = 16 тАУ x
According to the condition,
┬а
Either x тАУ 12 = 0, then x = 12
or x тАУ 4 = 0, then x = 4
(i) If x = 12, then
First number = 12
and second number = 16 тАУ 12 = 4
(ii) If x = 4, then First number = 4
and second number = 16 тАУ 4 = 12
Hence numbers are 4, 12

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