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.
Sonali said:
1 decade ago
I can't understand this step.
20x^2+25x-16x-20=0.
How it becomes 25x & 16x ?
Please explain.
20x^2+25x-16x-20=0.
How it becomes 25x & 16x ?
Please explain.
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?
Rani said:
1 decade ago
(4x + 5)(5x - 4) = 0.
4x + 5 = 5x - 4.
(5x-4x)+ 5 = 4.
x+5 = 4.
x = 4/5.
4x + 5 = 5x - 4.
(5x-4x)+ 5 = 4.
x+5 = 4.
x = 4/5.
Narasingarao said:
1 decade ago
What is meant by reciprocal and positive proper fraction? concept not cleared kindly help.
Sree said:
1 decade ago
What is meant by reciprocal?
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.
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.
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..
If we assume +proper fraction to be x then x-(9/20)=(1/x), and not as you said...
I think this is wrong..
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
then x will be 5/4 which is not in the options
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