Two particles A and B are projected from point O with equal speeds. They both hit the point P of an inclined plane of inclination 15o. Particle A is projected at an angle 30o with inclined plane. If the ratio of time of flight of particles A and B is 1:n. The value of n is ________.

∵y=uyt+12ayt2 Or  0=uyT−12gcos⁡30∘T2∴ T=2uygcos⁡30∘=4uy103∴ TA=4usin⁡15∘103      ......(i) and  TB=4usin⁡α103where, α is angle of projection of particle B,∵ R=uxT+12axT2     ......(ii) Or  R=ucos⁡60∘TA−12gsin⁡30∘TA2=(ucos⁡α)TB−12gsin⁡30∘TB2 Or  ucos⁡60∘×4usin⁡60∘103−12gsin⁡30∘TA2=(ucos⁡α)TB−12gsin⁡30∘TB2Putting the value of TA and TB,    α=90∘−15∘−30∘=45∘∴     TATB=4usin⁡30∘1034usin⁡α103=sin⁡30∘sin⁡α=2×12=12=1:n∴     n=2