Aptitude - Numbers - Discussion

Discussion Forum : Numbers - General Questions (Q.No. 26)
26.
The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
3
5
3
10
4
5
4
3
Answer: Option
Explanation:

Let the required fraction be x. Then 1 - x = 9
x 20

    1 - x2 = 9
x 20

     20 - 20x2 = 9x

     20x2 + 9x - 20 = 0

     20x2 + 25x - 16x - 20 = 0

     5x(4x + 5) - 4(4x + 5) = 0

     (4x + 5)(5x - 4) = 0

x = 4
5

Discussion:
53 comments Page 1 of 6.

Pratyush Sharma said:   1 year ago
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.
(2)

Kazibwe Moses said:   3 years ago
4/5 is wrong it will give us a negative answer.

If we are to prove it;
4/5-its reciprocal,
4/5-5/4 = ((16/25)/20) = -9/20.
(13)

Eternal said:   3 years ago
It's easy to try all the options in the given condition that is 1/x-x = 9/20.

Here, put x=4/5 in the above equation we get 9/20 so the answer is 4/5.

Hope you get it.
(7)

Ashutosh rusiya said:   4 years ago
Take x is a fraction number and 1/x would be its reciprocal number and x-1/x =9/20.
(2)

Shama M said:   4 years ago
Since they have mentioned proper fraction (which is always less than 1), we assumed the difference to be 1/x - x.
(2)

Shanu said:   4 years ago
Why 1-x^2/x? Please explain it.
(1)

Karthik said:   4 years ago
Please anyone explain me in detail.

Gayathri said:   4 years ago
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!
(2)

Saran Satz said:   4 years ago
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.
(7)

Nisha said:   5 years ago
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!
(3)


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