A source emits light of wavelengths 555 nm and 600 nm . The radiant...

The total luminous flux is the sum of the luminous fluxes for each wavelength.

The luminous flux for a given wavelength is calculated as $\Phi_v = 685 \times V(\lambda) \times \Phi_e(\lambda)$, where $V(\lambda)$ is the relative luminosity and $\Phi_e(\lambda)$ is the radiant flux.

At $555 \text{ nm}$, the relative luminosity is maximum, so $V(555 \text{ nm}) = 1$.

Luminous flux for the $555 \text{ nm}$ part:

$\Phi_{v1} = 685 \times 1 \times 40 = 27400 \text{ lumen}$

For the $600 \text{ nm}$ part, the relative luminosity is given as $V(600 \text{ nm}) = 0.6$.

Luminous flux for the $600 \text{ nm}$ part:

$\Phi_{v2} = 685 \times 0.6 \times 30 = 12330 \text{ lumen}$

Total luminous flux:

$\Phi_v = \Phi_{v1} + \Phi_{v2} = 27400 + 12330 = 39730 \text{ lumen}$