A water tank is filled in 5 hours by three pipes X, Y and Z the pipe Z is thrice as fast as Y and Y is twice as fast as X. How much time will pipe X alone take to fill the water tank?

A water tank is filled in 5 hours by three pipes X, Y and Z the pipe Z is thrice as fast as Y and Y is twice as fast as X.

$$ \frac{Z}{Y}=\frac{3}{1}  and  \frac{Y}{X}=\frac{2}{1} $$

Now equate both the ratios by making Y equal in both,

$$ \frac{Z}{Y}=\frac{6}{2} and \frac{Y}{X}=\frac{2}{1} $$

So, Z : Y : X = 6 : 2 : 1 (this is the ratio of efficiencies of the pipes)

If three pipes fill the tank in 5 hours, there fore the total work done is

$$=Time \times Total  Efficiency  of  pipes$$

$$=5\times (6+2+1) = 45$$

So X will take time = $$\frac{Work}{X's  efficiency}$$

$$=\frac{45}{1} = 45 hours$$

Option B is correct.