We studied the energy spectrum of two coupled XY spin-1/2 chains with different exchange integrals and inter-chain interaction of Ising type. The thorough analytical treatment of two-magnon states was given for finite and infinite lattice strips. To study the case of macroscopic number of inverted spins we used the corresponding density matrix renormalization group (DMRG) simulation. We also derived the self-consistent Bardeen-Cooper-Schrieffer (BCS) estimates for the lowest energies of the system. The comparison of the BCS and the DMRG estimates has shown incorrect behaviour of the BCS approximation for energy as a function of the intra-chain exchange integrals. To use the analytical results for two-magnon bound states we proposed a simple approximate formula for the lowest n-magnon energies of an infinite ladder with a more correct dependence on model parameters.