Aptitude - Numbers - Discussion

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.

Assume the fraction x/y.
Reciprocal becomes y/x.

According to condition,
x/y - y/x= 9/20,
on solving LHS we get.

(x^2- y^2)/(xy)= 9/20, Here x^2 means x square.

Hence we get (x+y)(x-y) / (xy) = 9/20.

Now we have to write 9 as a product of two numbers they can be
9 = 3x3 and 9 = 9x1.

Since 3x3 is not possible as sum and difference of 2 numbers.
Hence we have that,
(x+y)=4 and (x-y )=1.

Solution is x=4 and y=5.

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.

In the given case, 9/20 is the difference between the fraction and its reciprocal.

We know that the Denominator is always LCM of denominators of the fractions.
So, checking the possibility for 20: 1*20, 2*10, 4*5.
Since 1/20 and 2/10 are not possible because it is given that the first fraction is proper 20 - 1/20 will never yield 9/20.

So, the answer will be 4/5.

Hello everyone,

I hope this may help you.
Keeping all these X things aside, there is a simpler way.

Fraction means 4/5 and it's reciprocal is simply upside-down. That means 5/4. So here the difference is already given. So for each option, we just need to subtract the reciprocal of the same fraction.

So, 4/5-5/4 = 9/20.

As simple as that.
Thank you!

As per the question, y/x - x/y = 9/20,
(y2-x2) / xy = 9/20.
So, we can just take xy=20,
now check options, substitute the values of x & y.
option a) 3*5=15 (not equal to 20),
b) 3*10=30 (not equal to 20),
c) 4*5= 20 (bingo),
d) 4*3=12 (not equal to 20),
So, the answer is option C.

Simple Logic.

Give answer is 9/20 (If we do a difference for proper fraction and it's reciprocal).

We take LCM while calculating the difference between fractions and given answer is 9/20 and got LCM as "20".

So, check options which get LCM as 20.

And option 4/5 gives LCM 20 and that's it!

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.

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.

It's simple ----just inverse every fraction and calculate lcm of denominator of two fractions.
a) 3/5 - 5/3=denomator 20
b) 3/10- 10/3=30
c) 4/5 - 5/4=20
d) 3/4-4/3=12

At question different is 9/20 so, answer should be option B) 4/5.