x + (1/y) = 7/3 y + (1/x) = 7/2 x and y are non integer values then x*y = ?

M4maths Previous Puzzles

20 Apr 2012 non integers

x + (1/y) = 7/3
y + (1/x) = 7/2
x and y are non integer values
then x*y = ?

OPtion

1) 0.12
2) 0.125
3) 0.133
4) 0.14
5) 0.15
6) 0.16
7) 0.167
8) 0.2
9) 0.25
10) none of these

Solution

x + (1/y) = 7/3 or (xy+1)/y = 7/3 (1)
y + (1/x) = 7/2 or (xy+1)/x = 7/2 (2)
on dividing (2) by (1), we will get
x/y = 2/3
let x = 2k and y = 3k
then from (1) equation, [6(k^2)+1]/3k = 7/3
or k = 1 or 1/6
so x = 2 or 2/6 and y = 3 or 3/6
since x and y are non integers
so x = 2/6 = 1/3 and y = 3/6 = 1/2

Correct Option: 7 Best Solution (0)