If ` 5 x + 9 y = 5 and 125 x^(3) + 729 y^(3) = 120` then the value of the product of x and y is

Options

A. 123
B. 45
C. `(1)/(135)`
D. `(1)/(9)`

Answer

C

Explanation

`5x + 9y = 5`
`implies ( 5x + 9 y ) ^(3) = 125`
`implies 125 x ^(3) + 729 y ^(3) + 3. 5 x 9y (5x + 9y) = 125`
`implies 120 + 135 xy (5) = 126`
`implies 675 xy = 125 - 120 = 5`
`implies xy = (5)/(675) = (1)/(135)`