Cross sections of the 113In(n,2n)112m,gIn and 115In(n,2n)114m,gIn reactions and their isomeric cross-section ratios σmg have been measured by means of the activation technique at three neutron energies in the range 13 to 15 MeV. Indium samples and niobium monitor foils were activated together to determine the reaction cross section and the incident neutron flux. The monoenergetic neutron beam was produced via the 3H(d,n)4He reaction at the Pd-300 Neutron Generator of the Chinese Academy of Engineering Physics. The activities induced in the reaction products were measured using high-resolution gamma-ray spectroscopy. The pure cross section of the ground state was derived from the absolute cross section of the metastable state and the residual nuclear decay analysis. Cross sections were also evaluated theoretically using the numerical nuclear model code TALYS-1.8 with different level density options at neutron energies varying from the reaction threshold to 20 MeV. Results are discussed and compared with the corresponding literature.