From the top of a tower a stone thrown up it reaches the ground in 'n1sec' and a second stone thrown  down  from same tower with same speed it reach the ground in 'n2' sec. A third stone released from rest it reach the  ground in 'n3' sec then

The stone which is projected up  h=−Un1+12gn12            →(1)initial velocity=U; acceleration due to gravity=g; time elapsed=t; displacement=S=hThe stone which is projected down  h=Un2+12gn22        →(2)The stone which is dropped from tower  h=12gn32→(3) subtract equation (1)−(2)⇒0=−Un1−Un2+12gn12−12gn22⇒0=−Un1+n2+g2n12−n22⇒Un1+n2=g2n12−n22⇒2Ug=n1−n2⇒U=gn1−n22---(4)From 1:-  h=−Un1+12gn12substitute eqn (4)⇒h=−n1gn1−n22+12gn12⇒h=−g2n12+g2n1n2+g2n12⇒h=12gn1n2---(5) From 3:-  h=12gn32 substitute eqn (5)⇒12gn32=12gn1n2n3=n1n2