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Question

If twice the  reciprocal of a positive number is subtracted from the same number, we get 1. Find the number.
  1. 3
  2. 1
  3. 2
  4. 4


Solution

The correct option is C 2
Let the number be x.
Reciprocal of a number = 1x
Twice the reciprocal = 2x

According to the given condition,
x2x=1
x22=x
x2x2=0

Quadratic formula is given by,
x=b±b24ac2a

Here, a=1,b=1 and c=2

x=1±1(4×1×2)2

        =1±1+82

        =1±92

         =1±32

x=2 ,1

As the number is positive, ignore negative value.

Hence, x = 2
The required number is 2.

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