Problem Solving

in reservor two tube leaks, the first tube can fill an empty bucket in x hours, and the second tube alone can fill the same bucket in y hours, where x<y, if both tubes began leaking at the same time into the empty bucket at their respective constant rates and consequently it took t hours to fill the bucket, which of the following must be true?
I 0<t<y
II x<t<y
III x/2<t<y/2

I only
II only
III only
I and II only
I and III only

IMO its E

I. t hours must obviously be > 0 as the time taken cannot be -ve. And it also makes sense that it is less than y

II. This need not be true.
Assume, x=2, y=3,
1/2 + 1/3 = 5/6 or 6/5 hrs (t)
t < x < y. t need not be within the limits of x and y.

III. Tried few values (Lower and Higher) and this equation is satisfied.

Should be E

One more........ IMO (E)

IMO E

on solving we get a eqn t=xy/(x+y)

now trying with some no. satisfying the condition x<y such as x=2 and y=3;x=3 and y=4 ;x=4 and y=6

we get one and three possible