Aptitude - Numbers - Discussion

It should be x - 1/x = 9/20. Thus, x would come out to be 5/4.

The Best Way Is:
x/y - y/x = 9/20 (Given) -------------(1)

verify with options: I have done with option 4,.

Here x = 4,y = 5;
Substitute in (1)
4/5 - 5/4 = 9/20.
Then, l.h.s = r.h.s.

x = 4/5.

=> (1/x) - x = (5/4) - (4/5),

= (25-16) /20 =9/20 (+Positive).

=> x - (1/x) = (4/5) - (5/4),

= (16-25) /20 = -9/20 (-Negative).

I hope you will get this.

Why can't the fraction be represented as X/Y instead of just X? Can't the question be solved like my concept as;

Let positive fraction be X/Y.

Then the difference between the positive fraction and its reciprocal can be X/Y - Y/X = 9/20.

Please proceed the correct answer.

Thanks.

Very nice explanation, thank you all.

Positive proper fraction means: A number which is in p/q form where p is always less than q.

Let the positive proper fraction = x (It can be 1/3, 4/7, 6/9 anything).

And the reciprocal of this positive proper fraction = 1/x.

Now you are thinking why we do ((1/x)-x) = 9/20.

Why we can't do like (x)-(1/x) = 9/20?

Because x is a positive proper function. So its denominator is greater then numerator.

And when we take their reciprocal the numerator will become greater then numerator so 1/x is greater than x.

And that's why we take here ((1/x) -x) = 9/20.

And finally you will get the value of x, i.e. 4/5.

Can anyone tell me what is meaning of "positive proper fraction"?

Me too read all the answer but still I am not getting the answer please tell me what is positive proper fraction and how could you take the 25x-16x is there any logic.

I read all the answer and conversation but still I am not getting why they done 1/x - x = 9/20.

Please clear the confusion as above the first line of question. Ravi you tried good but as per the sentence x + 9/20 = 1/x.

Please explain how it become (5x-4) (4x+5) = 0?