Aptitude - Numbers - Discussion

I think the right answer is 5/4.

Ref: RS Agarwal.

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.

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.

The conventional approach will be the lengthy one for this question.
So by checking all the options we get the option (d),
i.e 5/4-4/5 = 9/20.

If the ans is 4/5.

4/5 - 5/4 should be 9/20 which is not right.. 4/5 - 5/4 is - 9/20.

The answer should be 5/4.

They told in question the difference between +ve proper fraction and its reciprocal is 9/20. Means -> Positive proper fraction=1/x and its reciprocal is 1/1/x=x. Their difference is (1/x) -x=9/20. So we have to find x. Find x by the above method.

@ Rima.

The numerator is less than the denominator.

Examples: 1/3, 3/4, 2/7. Improper Fractions: The numerator is greater than (or equal to) the denominator.

Positive proper function is in form of 1/x and its reciprocal is x that why we are considering 1/x - x = 9/20.

Answer should be 5/4 not 4/5.