Aptitude - Numbers - Discussion

20 - 20x2 = 9x.

20x2 + 9x - 20 = 0.

This part is really confusing if 9x is after = and if it is brought before =0 it should be - 9x.

Like 20x2 -9x + 20=0 !don't know I may be wrong but how you placed it please explain?

I can't understand this step.

20x^2+25x-16x-20=0.

How it becomes 25x & 16x ?

Please explain.

It is the concept of factorization of 10th std.

Difference of +25x-16x = 9x.

So, we can write (25x- 16x) in place of 9x so that we can factorize resulting equation, i.e.
20x^2+25x-16x-20 = 0.

Now in 1st two terms -20x^2 & 25x pick the common one out which is 5x
=5x(4x + 5).

Similarly in last two terms,common is 4.

So, whole equation will be,

5x(4x+5) - 4(4x + 5 ) = 0.

Therefore (5x-4)(4x+5) = 0.

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

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.

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.

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

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.

Very nice explanation, thank you all.

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.