In 1 hour, one train goes (21-16)= 5 km more than another.

Now, In 1 hour total distance covered by them = (16+21) km = 37 km

If distance difference is 5 km then total distance = 37 km

If distance difference is 60 km then total distance = $\left(\frac{37\times 60}{5}\right)=444$ km 

Distance between Dhaka and Chittagong is 444 km. (ans.)

$Here, relative speed of Y in terms of X$

$=\frac{4x}{3}-x=\frac{4x-3x}{3}=\frac{x}{3} mph.$

$X will cover in (11.30 - 10) = 1.5 hours = ( x \times 1.5) miles = 1.5x miles$

$\therefore Required time taken by Y to catch X= \frac{1.5x}{{\displaystyle \frac{x}{3}}}=1.5x\times \frac{3}{x}=4.5x hours$

$\therefore Y will meet X at =11.30 am +4.5 hour = 4 pm$

$Alternative: Given that,$

$X\text{'} s speed is = x mph$

$\therefore Y\text{'}s speed is =\frac{4x}{3} mph$

$Let, X and Y will meet after p hours$

$$\begin{gathered} According to questions, \\ px = (p - 1.5) \times \frac{4x}{3} [As, d = time \times velocity] \end{gathered}$$

$$\begin{gathered} =px=\frac{4px}{3}-2x \\ =\frac{4px}{3}-px=2x \\ =\frac{4px-3px}{3}=2x \\ =px=6x \\ \therefore p=6 \\ \therefore Y will catch train X at = 10 am +6 hours = 4pm \left(answer\right) \end{gathered}$$

First train speed v₁= 72*5/18 =20 ms^-1

Second train speed v₂=54*5/18=15 ms^-1

Required time=(100+120)/(20-15)=44 second