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Aptitude - Numbers - Discussion

Discussion Forum : Numbers - General Questions (Q.No. 26)
Numbers
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.
Gagan said:   1 decade ago
Wrong. Why did you take the resiprocal first why not the fraction which was mention first in the question?
Chetan said:   1 decade ago
How did you get (4x+5)(5x-4)=0 as x=4/5? Could you please explain?
Janu said:   1 decade ago
If we assume that the +ve fraction would be x

then x + (9/20) = 1/x (ex: x+y=z => y=z-x)

So (1/x) - x = (9/20)...

Hope you understand...
Janu said:   1 decade ago
Ofcourse if we take x-(1/x)=(9/20)

then x will be 5/4 which is not in the options
Anil said:   1 decade ago
@janu:

If we assume +proper fraction to be x then x-(9/20)=(1/x), and not as you said...

I think this is wrong..
Prateek said:   1 decade ago
As the ans is 9/20, it means lcm of numerator & denomenator should be 20. 4/5 only satisfies the above cond.
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.
Sree said:   1 decade ago
What is meant by reciprocal?
Narasingarao said:   1 decade ago
What is meant by reciprocal and positive proper fraction? concept not cleared kindly help.
Rani said:   1 decade ago
(4x + 5)(5x - 4) = 0.

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

x+5 = 4.
x = 4/5.
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