Find Apparent Magnitude of Binary Star System w/o Distance

[vivekdoulat]

Please could you let me know how to find out apparent magnitude of a star when you know the apparent magnitude of the binary star system?
p.s. the distance between the observer and the system is'nt given.

I have the luminosities of both the stars as well as absolute magnitudes of both the stars.

 

[Jolb]

Apparent magnitude of a star at a distance d depends on the flux F (of light) from the star through a unit area at that distance d. In other words, F=L/(4 pi d^2). Note that d appears in the equation. But it cancels if the distance of the two stars is the same (as in a binary) when computing the relative magnitudes.

Here's the formula for changing between fluxes and apparent magnitudes:
$$\frac{F_{1}}{F_{2}}=10^{0.4(m_{2}-m_{1})}$$