Let the velocity of the first body be V1,given that it is projected at an angle of 60
Let the velocity of the second body be V2,given that it is projected at an angle of 30
The given condition here is that the maximum height attained by both bodies is the same i.e Hmax is same for both of them
Let the maximum height attained by first body is Hmax-1 and maximum height attained by the second body is Hmax-2
We know that Hmax is equal
this implies that Hmax-1=Hmax-2
V
12sin
2
/2g=V
22sin
2
/2g
V12sin260=V22sin230
V12/ V22 =sin230/sin260
V
1/V
2=1/

3