Latest Book Aptitude Question SOLUTION: the difference between a positive fraction and its reciprocal is 9/20 find the sum of that fraction and its reciprocal.

• Placement Papers
• /
• Book

Book Question Papers:

(#M40021189) BOOK question Keep an EYE

the difference between a positive fraction and its reciprocal is 9/20 find the sum of that fraction and its reciprocal.

Asked In Book Abhishek (10 years ago)

Unsolved Read Solution (1)

Is this Puzzle helpful?   (2)   (0) Submit Your Solution

Read Solution (1) :

Rene  (10 years ago)

x = the number
1/x is the reciprocal of the number
-----
x - (1/x) = 9/20
multiply both sides by x to get:
x^2 - 1 = (9/20)*x
subtract (9/20)*x from each side of the equation to get:
x^2 - (9/20)*x - 1 = 0
multiply both sides of the equation by 20 to get:
20x^2 - 9x - 20 = 0
-----
using the quadratic formula of -b+-_/b^2-4ac / 2a gets me:
x = 50/40
or:
x = -32/40
-----
x = -32/40 is rejected because it is not positive and the problem stated that it had to be a positive fraction.
-----
your answer is x = 50/40 which is the same as:
x = 5/4

-----
to confirm this answer is correct, substitute in the original equations.
-----
if we let x = 5/4, then:
x - (1/x) = 9/20 becomes:

5/4 - 1/5/4 = 9/20
5/4 - 4/5 = 9/20

this is the same as:
%285%2F4%29+-+%284%2F5%29+=+9%2F20
this becomes:
25-16/20 = 9/20
which becomes:
9/20 = 9/20 confirming that x = 5/4 is good.
-----
your question was:
find the sum of the fraction and it's reciprocal.
-----
the answer is:
-----
if x = 5/4, then 1/x = 4/5 and the sum is 5/4 + 4/5 = (25+16)/20 = 41/20
-----

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.