At how many distinct points in a watch do the hour and

Solution

ATQ, First time at 0 degree when minute hand travels 360, then hour hand travels 360/12 or 30, thus for every 1 degree of hour hand, minute hand travels 360/12 or 30 degree. So next time when hour hand is at 1 or 30 degree, let them meet after hour hand moves x degrees =>( 30 + x )= (0 + 12 × x)....(11x = 30)...(x = 30/11). Thus the point is 30 + (30/11)=30(12/11).. Similarly when hour hand is at 2 or 60 degree, let them meet after hour hand moves x degrees = 60 + x = (0 + 12) × 'x'....11x =60...x = (60/11) Thus the point is 30 + (30/11) = 30(12/11) So ('x'× 30)(12/11)<= 360......'x'<= 11 Hence 11