find the maximum of the DFT of sampled signal
Note that the frequencies of the FFT grid are given by

$$f_k=\frac{kf_s}{N},\qquad k=0,1,.\ldots,N-1\tag{1}$$

where $N$ is the FFT length.

Now observe that the two frequencies of the given signal fall exactly on the grid. So you only have to determine these two frequencies, and then use $(1)$ to figure out the corresponding indices.


EDIT:

It's always good to check your results using some simulation software. The following Octave/Matlab script confirms what you came up with.


phi = 0;    % exact value irrelevant
n = 0:99;
T = 1/25;
y = cos( 10*pi*n*T+phi ) + cos( 20*pi*n*T );
Y = fft(y);
subplot(2,1,1), plot(n,abs(Y),'x'), grid on