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 5 of 6.
Poornamsh said:
1 decade ago
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.
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.
Saurin said:
9 years ago
Thank you all.
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.
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.
Rima said:
1 decade ago
Can anyone tell me what is meaning of "positive proper fraction"?
Nikita said:
10 years ago
Very nice explanation, thank you all.
Jigdrel said:
10 years ago
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.
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.
Md Kashif said:
9 years ago
It should be x - 1/x = 9/20. Thus, x would come out to be 5/4.
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.
Prithviraj chauhan said:
9 years ago
You can take it as, a/b - b/a = 9/20.
a2 - b2 /ab =9/20 then equate ab = 20 options are 1 * 20, 2 * 10, 4 * 5 and here we get our answer guys.
a2 - b2 /ab =9/20 then equate ab = 20 options are 1 * 20, 2 * 10, 4 * 5 and here we get our answer guys.
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