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 6 of 6.
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.
Gagan said:
1 decade ago
Wrong. Why did you take the resiprocal first why not the fraction which was mention first in the question?
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