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:
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 2 of 6.
Anomi said:
7 years ago
It must be x-1/x=9/20 in the first place.
Since +ve proper fraction x is always greater than it's reciprocal. For eg if we consider 3 as +ve proper fraction, then it's reciprocal is 1/3 which is obviously lesser than 3.
Since +ve proper fraction x is always greater than it's reciprocal. For eg if we consider 3 as +ve proper fraction, then it's reciprocal is 1/3 which is obviously lesser than 3.
Silvester said:
1 decade ago
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?
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?
Nitu said:
1 decade ago
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 clear the confusion as above the first line of question. Ravi you tried good but as per the sentence x + 9/20 = 1/x.
Krishna Sowjanya said:
6 years ago
Let the proper fraction be x/y.
Then (x/y)-(y/x) = 9/20.
LCM of x and y = xy.
Therefore the denominator xy =20 obviously.
So, by cross-checking the options in option C we have 4 * 5=20. i.e., x=4 and y=5.
Then (x/y)-(y/x) = 9/20.
LCM of x and y = xy.
Therefore the denominator xy =20 obviously.
So, by cross-checking the options in option C we have 4 * 5=20. i.e., x=4 and y=5.
(1)
Bhaski said:
1 decade ago
How can ans be C ?
Let us assume the fraction be x/y.
then x/y-y/x=9/20
x^2-y^2>0 //since 9/20 is positive and xy is positive...
so obviously x>y.
numerator>denominator.
Let us assume the fraction be x/y.
then x/y-y/x=9/20
x^2-y^2>0 //since 9/20 is positive and xy is positive...
so obviously x>y.
numerator>denominator.
Sai said:
9 years ago
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/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.
(1)
Kavitha said:
9 years ago
In the question, it was mentioned that difference between fraction and its reciprocal is 9/20.
So let the fraction be 1/x
Then its reciprocal is 1/(1/x) = x
Therefore, 1/x - x = 9/20.
So let the fraction be 1/x
Then its reciprocal is 1/(1/x) = x
Therefore, 1/x - x = 9/20.
Eternal said:
4 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.
Here, put x=4/5 in the above equation we get 9/20 so the answer is 4/5.
Hope you get it.
(9)
Aparna said:
1 decade ago
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.
Akhilkondaparva said:
9 years ago
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.
=> (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.
(1)
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