arithmetic - two trains one from howrah to patna and the other from patna to howrah start simultaneously after they meet the trains reach their destinations after 9 hours and 16 hours respectively the ratio of their speeds is - skillgun

Suppose the total distance is x,
Time taken by trains to meet = t
if speeds be s1 and s2, and they meet after time t,
=> s1*t + s2*t =x (eqn 1)
Train A takes total t+9 hours to travel x with speed s1,
=> s1(t+9)=x (eqn 2)
for train B, total time t+16
=> s2(t+16)=x (eqn 3)
9*s1= t*s2 (equate eqn 1 and 2)
t*s1= 16*s2 (equate eqn 1 and 3)
divide,
9/t= t/16 => t*t= 9*16
substitute t,
=> s1/s2= sqre-root (16/9)