Two trains each having a length of 160 meters moving in opposite direction crossed each other in 9 seconds. If one train crossed a 200-metre-long platform in 18 seconds,then the ratio of their speeds is:

Two trains each having a length of 160 meters moving in the opposite directions crossed each other in 9 seconds.

Let's assume the speed of trains are 'a' and 'b' respectively.

$$\frac{\left(160+160\right)}{a+b}\ =\ 9$$

$$\frac{320}{9}\ =\ \left(a+b\right)$$    Eq.(i)

If one train crossed a 200 metre long platform in 18 seconds.

speed of one train = a = $$\frac{\left(160+200\right)}{18}$$

= $$\frac{\left(360\right)}{18}$$

= 20 m/s    Eq.(ii)

Put Eq.(ii) in Eq.(i).

$$\frac{320}{9}\ =\ \left(20+b\right)$$
$$\frac{320}{9} - 20 = b$$

$$\frac{320-180}{9}=b$$

$$\frac{140}{9} = b$$    Eq.(iii)

Ratio of their speeds is: Eq.(ii) : Eq.(iii)

$$20 : \frac{140}{9}$$

$$1 : \frac{7}{9}$$

9 : 7