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 3 of 6.
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)
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)
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.
Pawas said:
9 years ago
Assume the fraction x/y.
Reciprocal becomes y/x.
According to condition,
x/y - y/x= 9/20,
on solving LHS we get.
(x^2- y^2)/(xy)= 9/20, Here x^2 means x square.
Hence we get (x+y)(x-y) / (xy) = 9/20.
Now we have to write 9 as a product of two numbers they can be
9 = 3x3 and 9 = 9x1.
Since 3x3 is not possible as sum and difference of 2 numbers.
Hence we have that,
(x+y)=4 and (x-y )=1.
Solution is x=4 and y=5.
Reciprocal becomes y/x.
According to condition,
x/y - y/x= 9/20,
on solving LHS we get.
(x^2- y^2)/(xy)= 9/20, Here x^2 means x square.
Hence we get (x+y)(x-y) / (xy) = 9/20.
Now we have to write 9 as a product of two numbers they can be
9 = 3x3 and 9 = 9x1.
Since 3x3 is not possible as sum and difference of 2 numbers.
Hence we have that,
(x+y)=4 and (x-y )=1.
Solution is x=4 and y=5.
Akshat said:
8 years ago
The conventional approach will be the lengthy one for this question.
So by checking all the options we get the option (d),
i.e 5/4-4/5 = 9/20.
So by checking all the options we get the option (d),
i.e 5/4-4/5 = 9/20.
Imtiyaj said:
8 years ago
It's simple ----just inverse every fraction and calculate lcm of denominator of two fractions.
a) 3/5 - 5/3=denomator 20
b) 3/10- 10/3=30
c) 4/5 - 5/4=20
d) 3/4-4/3=12
At question different is 9/20 so, answer should be option B) 4/5.
a) 3/5 - 5/3=denomator 20
b) 3/10- 10/3=30
c) 4/5 - 5/4=20
d) 3/4-4/3=12
At question different is 9/20 so, answer should be option B) 4/5.
Saurin said:
8 years ago
Thank you all.
Samyuktha said:
8 years ago
If the ans is 4/5.
4/5 - 5/4 should be 9/20 which is not right.. 4/5 - 5/4 is - 9/20.
The answer should be 5/4.
4/5 - 5/4 should be 9/20 which is not right.. 4/5 - 5/4 is - 9/20.
The answer should be 5/4.
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